Distributed Source Coding and Its Applications in Relaying-Based Transmission

Received January 10, 2016, accepted January 26, 2016, date of publication March 2, 2016, date of current version May 11, 2016.

Digital Object Identifier 10.1109/ACCESS.2016.2537739 Distributed Source Coding and Its Applications in Relaying-Based Transmission

ABDULAH JEZA ALJOHANI, SOON XIN NG, (Senior Member, IEEE), AND LAJOS HANZO, (Fellow, IEEE) University of Southampton, Southampton SO17 1BJ, U.K. Corresponding author: L. Hanzo ([email protected]) This work was supported in part by the European Research Council within the BeamMeUp Project, in part by the U.K. Engineering and Physical Sciences Research Council under Grant EP/Noo4558/1 and Grant EP/L018659/1, in part by the Saudi Ministry of Higher Education and in part by the Royal Society’s Wolfson Research Merit Award.

ABSTRACT Distributed source coding (DSC) schemes rely on separate encoding but joint decoding of statistically dependent sources, which exhibit correlation. DSC has numerous promising applications ranging from reduced-complexity handheld video communications to onboard hyperspectral image coding under computational limitations. The concept of separate encoding at the first sight compromises the attainable encoding performance. However, the DSC theory proves that independent encoding can in fact be designed as efficiently as joint encoding, as long as joint decoding is allowed. More specifically, distributed joint source- channel coding (DJSC) is associated with the scenario, where the correlated source signals are transmitted through a noisy channel. In this paper, we present a concise historic background of DSC concerning both its theory and its practical aspects. In addition, a series of turbo trellis-coded modulation (TTCM)-aided DJSC-based cooperative transmission schemes are proposed. DJSC scheme is conceived for the transmission of a pair of correlated sources to a destination node (DN). The first source sequence is TTCM encoded, and then, it is compressed before it is transmitted both over a Rayleigh fading channel, where the second source signal is assumed to be perfectly decoded side-information at the DN for the sake of improving the achievable decoding performance of the first source. The proposed scheme is capable of performing reliable communications for various levels of correlation near to the theoretical Slepian–Wolf/Shannon (SW/S) limit. Pursuing our objective of designing practical DJSC schemes, we further extended the above-mentioned arrangement to a more realistic cooperative communication system, where the pair of correlated sources are transmitted to a DN with the aid of a relay node (RN). Explicitly, the pair of correlated source sequences are TTCM encoded and compressed before transmission over a Rayleigh fading multiple access channel, where our proposed scheme is capable of operating within 0.55 dB from the SW/S limit for a correlation coefficient value of ρ = 0.8, and within 0.07 bits of the minimum SW compression rate. The RN transmits both users’ signal with the aid of a powerful superposition modulation technique that judiciously allocates the transmit power between the two signals. The correlation is beneficially exploited at both the RN and the DN using our powerful iterative joint decoder, which is optimized using extrinsic information transfer characteristics charts.

INDEX TERMS Distributed joint source coding, distributed source coding, Slepian-Wolf Coding, joint source-channel decoding, TTCM, superposition modulation.

I. INTRODUCTION both satellites, which are referred to as STEREO Ahead Let us commence by considering the stereographic images and STEREO Behind, is shown in Fig. 2. On the 20th of of the Sun in Fig. 1, which were captured using a pair September 2013 they were more than 50 million km away of satellites that are part of NASA’s Solar Terrestrial from each other. In such a scenario, is it not readily fea- Relations Observatory (STEREO) project.1 The location of sible for them to communicate with each other. Similarly, each satellite has very limited communications with planet 1The STEREO project aims for providing revolutionary stereoscopic imaging of the sun in order to reveal the solar surface activities, such as the Earth [1], [3]. Thus, the employment of source compression Coronal Mass Ejection (CME) [1], [2]. is desirable, but the encoding of images has to be carried

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FIGURE 1. Stereographic solar images taking by NASA’s both STEREO satellites Ahead and Behind c NASA [1]. (a) STEREO Ahead solar image. (b) STEREO Behind solar image.

FIGURE 3. Decoded stereographic images of Fig. 1 after transmission over uncorrelated Rayleigh fading channels at SNR = 1.0 dB. (a) Ahead view, DJSC of Sec. V-B. (b) Behind view, DJSC of Sec. V-B. (c) Ahead view, non-DJSC benchmark of Sec. V-B. (d) Behind view, non-DJSC benchmark of Sec. V-B.

attaining perfect images recovery. By contrast, for the same amount of transmit power, both the Ahead and Behind images were severely corrupted upon using exactly the same coding FIGURE 2. Positions of both STEREO satellites Ahead and Behind scheme dispensing with joint decoding. Thus, exploiting the recorded on the 20th September 2013 c NASA [1]. correlation between the images by jointly decoding them has lead to a significant power reduction, while maintaining reliable communication. This room for improvement can be out separately at the satellites, while decoding may be car- also utilised for further source sequence compression, as it is ried out jointly at the Earth station, where both the power going to be illustrated in the subsequent sections. and computational constraints are relaxed. Intuitively, separate encoding would only allow separate compression of the II. DISTRIBUTED SOURCE CODING images of the distant satellites even though there is substantial DSC refers to the problem of compressing several phys- correlation between their images. However, the Distributed ically separated, but correlated sources, which are unable Source Coding (DSC) theorem of [4] states that separate to communicate with each other by exploiting that the encoding may be invoked instead of joint encoding without receiver can perform joint decoding of the encoded any loss of compression efficiency as long as the correlation signals [3], [4], [7]–[9]. However, Distributed Joint Source- among the sources is preserved throughout their transmission Channel coding (DJSC) is specific to the case, when the to the receiver, provided that they are jointly decoded [4]–[6]. correlated sources signals are transmitted over noisy chan- To offer a glimpse on the benefits of applying the DSC nels [8], [10]–[17]. More explicitly, a single channel code technique, we have separately encoded both satellite views of is employed for both source compression (via Slepian-Wolf Fig. 1 before their transmission over a uncorrelated Rayleigh Coding (SWC)) and channel error protection. Typically, the 2 fading channel. As Fig. 3 illustrates, when joint decoding is channel code in DJSC schemes is jointly designed to per- activated by invoking our decoder of Sec. V-B.1, no higher form both source compression as well as error protection. than 1.0 dB Signal-to-Noise Ratio (SNR) is required for Intuitively, the joint source-channel coding approaches would be less powerful than their separate counterparts [10], [11]. 2Both images were encoded separately using 1/2-rate Turbo However, this deficiency could be compensated through Trellis-Coded Modulation (TTCM) and decoded jointly using the decoder of Sec. V-B which is illustrated in Fig. 26, readers can have a quick look at exploiting the correlation between the sources at the joint Table 8 for main simulations parameters summary. decoder [10], [11].

VOLUME 4, 2016 1941 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

For both DSC and DJSC schemes the ultimate goal is to exploit the existing correlation for the sake of minimis- ing the transmission energy required by the sources, while maintaining reliable communication. From an architectural perspective, distributed techniques may be categorised into two main families [3], [10], [18], namely the class of operating in the presence of perfect side-information and in the absence of perfect side-information schemes. The schematic of the former [3], [9], [18] is shown in Fig. 4, where the source sequence {b1} is compressed before its transmission, { } FIGURE 5. Schematic diagram of dispensing with perfect while the correlated source signal b2 is assumed to be side-information DSC. ﬂawlessly available at the decoder, but not at the source {b1}. By contrast, in the scenario dispensing with perfect side- information both sources are compressed at a rate lower than their corresponding entropy rates, in which any point between the locations A and B of Fig. 7 can be reached. A special case of the latter scenario, when both users are compressed at the same rate, represented by point C in Fig. 7. The encoder has to compress {b1} without knowing {b2}, yet the decoder is capable of exploiting the knowledge of {b2} for recovering {b1}.

FIGURE 4. Schematic diagram of relying on perfect side-information DSC.

The rest of the paper is organised as seen in Fig. 6. Explicitly, the main principles as well as the historical background concerning both the theory and practice of DSC are presented in Sec. II. Then, our source correlation model is illustrated in Sec. III. Next, in Sec. IV we discuss our DJSC scheme under the idealized simplifying assumption of having FIGURE 6. Paper structure. perfect side information, before conceiving our cooperative DJSC scheme in Sec. V. Finally, we conclude our discourse in Sec. VI. in Fig. 7 this bound is identical, regardless whether joint A. SLEPIAN-WOLF THEORY encoding is used, i.e. regardless of where the joint processing The Slepian-Wolf (SW) theorem [4] has laid down the theo- takes place. Note that at the corner points shown in Fig. 7, retical foundations of DSC through specifying the achievable namely A and B, the SWC problem would be reduced to rate regions of the compressed correlated sources. Let us the scenario relying on perfect side-information, of Fig. 4. consider the arrangement of Fig. 5, where both {b } and {b } Using conventional lossless coding at rate of R2 = H(b2), for 1 2 { } are random sequences of independent and identically dis- example, will make b2 available at the joint decoder, thus tributed, i.i.d, samples. Upon their separate encoding and approaching point A. Later in 1976, the aforementioned loss- joint decoding, the SW theorem [4] states the rate region as: less SWC problem of [4] was extended to a lossy source coding problem relying on side-information at the decoder [5], R1 ≥ H(b1|b2), (1) which is widely known as the Wyner-Ziv Coding (WZC) R2 ≥ H(b2|b1), (2) problem [7], [10], [19]. More explicitly, the WZC problem asks the question of how many bits are required for encod- R1 + R2 ≥ H(b1, b2), (3) ing {b1}, when the side-information {b2} is perfectly known where H(b1|b2) and H(b1, b2) denote the conditional and at the decoder, while maintaining a speciﬁc level of distortion joint entropies, respectively. Remarkably, and as shown concerning {b1} at the receiver. These promising theoretical

1942 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

TABLE 1. Summary of major contributions on the theoretical fundamentals of lossless DSC.

optimal for point-to-point communication, as shown by Shannon, it will lead to a catastrophic error propagation in realistic Multiple Access Channel (MAC) scenarios. In [23] Cristescu et al. considered the scenario of a large set of correlated sources communicating with a set of destinations, where the problem of finding the optimal transmission structure was studied and the optimal rate allocations were found with the aid of SWC. In order to maximise the throughput of such a system, according to [23], two steps have to be invoked; first the optimal network structure has to be found; then the optimal rate allocation can be determined by solving an optimisation problem under linear constraints that are constituted by the SW rate region. In [25] the outage probability of transmitting two correlated sources with the aid of a Relay Node (RN) was evaluated, where the signals of the users were combined with the aid of a simple network coding scheme by FIGURE 7. Graphical representation of SW bound, using Eqs. (1)-(3). means of ⊕ operation. The major contributions made in the lossless DSC area are summarised in Table 1. results have led to intense research activities from both theoretical as well as from practical perspectives. B. WYNER-ZIV THEORY Cover [20] generalised the SWC problem by deriv- When considering lossy coding scenario, the WZ problem [5] ing the rate region bounds for more than two users, and asks the question of how many bits are necessary for encoding showed that the SW theorem can also be applied to non- the source {b1}, provided that the side-information {b2} is binary ergodic sources. It was stated in [22] that to opti- flawlessly known at the decoder. Thus, with the aid of Fig. 4, mise the overall performance, it is necessary to design the WZ problem can be characterised by the average distor- the source’s codewords having in mind the existence of tion expression of: the correlation. Additionally, it was stated in [22] that although the source and channel coding separation is indeed E d(b1,bb1) ≤ D, (4)

VOLUME 4, 2016 1943 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

FIGURE 8. Schematic diagram illustrates the MultiTerminal (MT) coding problem. where E [·] is the expectation operation, D is the maximum where the potential computational complexity has been acceptable distortion level and d(b1,bb1) denotes the distor- moved from the battery-limited sources to the central decoder tion function, which is widely chosen as the mean-squared connected to the mains supply [3], [7], [8], [28]. As a con- 2 error function b1 −bb1 [19]. Accordingly, the maximum sequence, the critical power constraint, which directly pre- compression rate that is achieved for this problem can be determines the operational life-span of a wireless node is formulated as [5]: satisfied [7], [8], [37]. The first practical SWC technique was proposed by Pradhan and Ramchandran [38], which was R ( ) = inf I (b ; Z | b ) , (5) 1 D 1 2 extended in [6], where both sources {b1} and {b2} are assumed to be emitting equiprobable codewords, but they exhibit a where inf is the mutual information infimum, i.e. the lower correlation, and {b } is only known to the joint decoder but bound, which is calculated over all possible random variables 2 not to the encoder of {b }. Naturally, this assumption does not of the set Z, in which the notation of b → b → Z 1 2 1 preclude that the codewords of {b } are actually received from defines a Markov chain.3 In 1985 [26], Heegard et al. have 2 a remote source, but they must be first perfectly recovered extended the WZ problem to more than two users. In his in isolation, before they may be used by the joint decoder insightful tutorial [27], Zamir et al. proposed the employ- for recovering {b }. Then, all legitimate codewords of both ment of nested lattice quantization for WZC. However, this 1 sources are grouped into cosets, where the members of each lattice quantizer is only asymptotically optimal, as the size coset are separated by the maximum possible Hamming dis- of the source dimensions tends to infinity, making it imprac- tance. Given {b } at the receiver, it is sufficient to transmit the tical to implement [10], [28]. Fig. 8 illustrates a so-called 2 index of the specific coset hosting the codewords of {b }. The MultiTerminal (MT) source coding problem, where the 1 decoder then estimates the transmitted codeword by opting encoders only have access to a distorted imperfect version for the one that is closest to the side-information constituted of the original sequences [10], [28]. As suggested by the by {b } of a given coset in terms of the Hamming distance d . figure, the problem may be categorised into two different 2 H For example, consider the DSC scheme of Fig. 4 relying classes. The first is the direct MT source coding problem on perfect side-information, where the correlated sources when the sensors interested in transmitting and estimating the {b } and {b } are of 3-bit length, i.e. {b } and {b } ∈ noisy versions of the source directly [29], [30]. By contrast, 1 2 1 2 {000, 001, 010, 011, 100, 101, 110, 111}. Due to the sources’ in the second case the system has no direct access to noisy correlation, at a specific time instant i, bi and bi differ versions of the source, but it rather has to estimate them at 1 2 at most in one position, i.e. their Hamming distance obeys the receiver [31]–[33]. The major works concerning the theo- di ≤ 1. Subsequently, the SW encoder groups all possible retical fundamentals of the lossy DSC are surveyed in Table 2. H codewords into cosets, whose members are separated by the maximum possible Hamming distance, thus we have: C. PRACTICAL ISSUES Applying DSC techniques in wireless sensor networks, S = [S00, S01, S10, S11] for example, has led to a new processing paradigm, = [{000, 111}, {001, 110}, {010, 101}, {100, 011}], (6)

3Further fundamental insights on lossy source coding can be found where each coset is colour coded similar to Fig. 9. The in [19, Ch. 1]. encoder in this scenario would transmit the index of the coset

1944 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

TABLE 2. Summary of major contributions to the theoretical foundations of lossy DSC.

To elaborate a little further, consider the real-world application example shown in Fig. 10, where the temperature of two nearby cities are transmitted to a joint decoder at the central weather-station. Similar to the aforementioned binary example of Fig. 9, both encoders group all possible codewords into disjoint cosets. One of the sensors, say Y , would transmit its reading using a full representation of say 6-bit symbols, while sensor X would only send the 2-bit index of the specific coset its reading belongs to, as illustrated at the top left corner of Fig. 10. The joint decoder will then exploit the correlation between the pair of temperatures by comparing the sensor signal Y to each member of the partic- ular coset represented by the specific 2-bit index transmitted by sensor X and finds that only the coset entry of X = 9 is FIGURE 9. The geometric realisation of the cosets given in Eq. (6). sufficiently similar to Y = 8 to satisfy their correlation. Thus a beneficial rate-reduction of 6−2 = 4 bits per sample can be i containing b1 using 2 bits rather than using 3 bits, while attained. i the decoder would recover b1 correctly with the help of Observe from Fig 9 and Fig 10 that, the correlation between i the side-information b2 . With reference to Fig. 9, assume the sources may be interpreted as the ameliorating effect of i = for example b1 100. Then, the index of the coset S11, a ‘‘virtual’’ channel. Hence, a good channel code having namely 11, will be transmitted. Now provided that we know for example a maximum minimum Hamming distance is i = i if b2 000, the decoder will compare b2 with each also expected to be a good SW code [10], [28], [39]. Thus, member of the coset S11 and then opts for the one having invoking powerful channel codes, such as turbo codes [40] i the lowest Hamming distance member from b2 . Hence, and Low-Density Parity-Check (LDPC) [41] is capable of i = the decoder concludes that b1 100 was transmitted by yielding a significant performance enhancement [7], [8]. i exploiting the side-information knowledge of b2 and its A DSC-aided syndrome bit-generation-based LDPC code i correlation with b1 . relying on perfect side-information system was studied

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FIGURE 10. Example of compressing correlated sources using DSC principles [28]. (a) DSC schematic. (b) UK temperature map. in [17] and [42]–[44], while a realistic imperfect side- information provision was investigated in [17], [44], and [45]. As stated previously, when transmitting correlated sources over noisy channels, the DSC problem is converted into a DJSC one [3], [8], [10]. The first practical DJSC scheme was proposed by Garcia-Frias in [46]. Similar to the DSC philosophy, depending on the architecture considered, DJSC has been presented in the literature in the context of two different scenarios [8], [10]. The first one is perfect side- information case, when the side-information is constituted by the source {b2} is perfectly shown at the decoder and is used for assisting in the decoding of the source {b1} transmitted over the noisy channel. In this scenario, it was shown in [47] that the entropy of the source of H(b1) in a conventional FIGURE 11. The main challenges when designing DSC schemes [28], [37]. point to point transmission should be replaced by H(b1|b2). Various schemes relying on perfect side-information-aided dashed lines, as it will be detailed in the subsequent sections. DJSC have been proposed in [9] and [48]–[50], where the Explicitly, these challenges can be summarised with the aid channel codes, such as turbo and LDPC codes, can also of Fig. 11 as [28], [37]: be adapted similarly to the above-mentioned DSC designs. 1) Correlation Estimation: in practice the statistical In the second case, known as the MAC scenario, the cor- dependence i.e. the correlation, between the sources related sources {b1} and {b2} are transmitted over a MAC, varies in time, and typically the decoding process where the separation principle does not hold [22]. Practical involves iterative information exchange between the DJSC schemes designed for the MAC transmission scenario constituent components of the joint decoder. This have been proposed in [14] and [51]–[54]. exchanged information has to be updated with the aid Apart from sophisticated channel coding design, many of an accurate correlation coefficient in order to avoid other aspects have to be carefully considered when conceiv- misleading the decoder [55]–[59]. ing a DSC scheme. Figure 11 illustrates the main challenges 2) Reduced-Complexity design: the main goal of to be circumvented, where the challenges that are consid- DSC-based schemes is to reduce the overall ered in this work are represented by ellipses printed using complexity, rather than only at the uplink

1946 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

transmitter side. For example, when considering a Distributed Video Coding (DVC) scheme for wireless transmission, real time decoding relaying on a low-complexity receiver is highly desirable [2], [44], [60], [61]. 3) Rate-Adaptive design: as stated in the first item, the correlation coefficient value varies in time. Addition- ally, the channel quality also fluctuates, when encoun- tering a fading channel for example. Thus, schemes that are capable of adapting their coding rates and (or transmission rates) in response to these variables have to be found [3], [18], [43], [49], [62]. 4) DJSC: intuitively any practical scheme has to be evaluated for transmission over realistic imperfect channels [14], [49], [52], [54]. FIGURE 13. The number of publications using the search term 5) Coded-Stream Compression: specially when consider- ‘‘Distributed Source Coding’’ and ‘‘Distributed Video Coding’’ in the ing realistic imperfect channels transmission, i.e. when Google Scholar web search engine from the calendar year 2005 to 2015. considering DJSC schemes. Puncturing the coded sequences in these scenarios still remains a persistent challenge [10], [49], [52], [63]. 6) Cooperative System design: cooperative techniques are capable of either achieving a diversity gain or enhancing the overall scheme’s throughput [64]–[66]. Given this rationale, several relay-aided DSC schemes were conceived in [15], [53], and [67]–[71].

D. OTHER SELECTED APPLICATIONS FIGURE 14. Schematic diagram illustrates the DVC proposed Although the DSC research was established in the realms of in [72] and [73]. information theory, recently both communication theory and image processing have also contributed to this field, because The number of publications during the last decade includ- DSC offers efficient solutions in diverse applications where ing both DSC and Distributed Video Coding (DVC) terms the sources exhibit correlation. The stylised illustration of is depicted in Fig. 13, indicating a substantial number of Fig. 12 portrays the relationship of DSC to its theoretical contributions. Hence, we briefly portray the state-of-the- background seen at the left of its diverse applications at the art in the subject area of DVC. The standard video codecs right [37]. including MPEG-2, H.263 and H.264 tend to have a high complexity encoder and a low complexity decoder [74]. More explicitly, in conventional video encoders a limited set of video frames, known as key frames, are encoded individually without involving other frames, which are referred to as intra- coded frames. The remaining predicted or intra-coded frames are encoded with reference to one or more previously encoded key frames, with the aid of motion-compensation, thus impos- ing a high-complexity at the encoder [3], [74]. This unequal distribution of complexity may be undesirable for emerging applications, such as wireless video sensor networks [7], [75], where both the energy and the computational complexity of the transmitter are constrained. In this context, DVC, also known as WZ video coding, offers a new processing approach, where the high computational complexity of temporal redundancy reduction relying on motion-compensation is transferred from the encoder to the powered by the mains decoder [3], [73], [76], [77]. To elaborate further, let us consider the DVC scheme of [72] and [73] shown in Fig. 14, where the WZ encoder

FIGURE 12. Stylised relationship of DSC to its theoretical is seen to consist of a SW encoder-based turbo encoder [40] foundations (left) and applications (right). following a quantization block, as justiﬁed below.

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TABLE 3. Summary of major contributions on DVC schemes.

The odd-indexed video frames X2i−1, known as key frames, Motivated by the above discussions, DSC techniques have are intra-coded using a conventional video codec, such as the been adopted in diverse applications, as illustrated in Fig 12. H.263/4 schemes of the lower branch in Fig. 14. By contrast, Albeit they are beyond the scope of this paper, there is a the even frames X2i, known in the DVC context as WZ frames, significant number of related contributions in the context of are encoded by the WZ codec seen in the upper branch of Distributed Audio Coding (DAC) [19], [89]–[92], hyperspec- Fig. 14. The WZ frames are being quantized for example tral image coding [2], [60], [61], [93]–[95], media authenti- to 8 bits/pixel and encoded using a turbo code, where only cation [96]–[100], securing biometric data [101]–[104] and the parity bits are transmitted incrementally upon request wireless sensor networks [7], [15], [23], [53], [67]. by the feedback channel to the receiver. At the receiver, the side-information of the WZ frames will be estimated from their adjacent key frames using joint inter-frame deco- E. RELATED WORKS ding [72], [73]. By doing so, the encoder avoids the com- As stated in Sec. II-C, the idea of using channel coding tech- plexity of motion search and motion-compensation amongst niques has enabled practical solutions to be developed, where the consecutive frames, while the decoder will assume the the correlation between the sources is modelled by invok- additional burden of constructing statistically dependent side- ing the philosophy of a Binary Symmetric Channel (BSC). information frames Y2i. Numerous solutions have been proposed based on novel For the sake of avoiding provision of the aforementioned channel codes. More specifically, turbo codes were proposed feedback channel which might preclude application of DVC for example in [9], [105], and [106], whereas Low-Density in delay-sensitive services, an LDPC-based scheme was Parity-Check (LDPC) codes were considered in [42]–[44]. proposed in [43] which formed the basis of the so-called However, these contributions relied on the idealised simpli- DIStributed COding for Video sERvices (DISCOVER) fying assumption of having noiseless auxiliary genie channel codec [77]. As further development, significant improvement between the source nodes and the base station. Whilst, the were added to the DISCOVER codec by enhancing both the separate design of source and channel coding was shown to be side-information construction [78]–[80] and by including an optimal by Shannon [8], [51] where perfect entropy-coding accurate correlation statistics estimation between the key and and capacity-achieving Forward Error Correction (FEC) WZ frames [81], [82]. Table 3 illustrates briefly the major codes are used, provided that both a potentially infinite contributions to DVC research. delay and an infinite complexity are acceptable, in practical

1948 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

multi-user fading channels they have limited applicability. III. CORRELATION MODEL Indeed, they would lead to catastrophic error propagation Typically the BSC-based abstraction is used for mod- in realistic MAC scenarios, as illustrated in [8] and [22]. elling the correlation between the two source sequences { } = { 1 2 ··· i ··· N } { } = { 1 2 ··· Several solutions were proposed for similar scenarios relying b1 b1, b1, , b1, , b1 and b2 b2, b2, , on the design of DJSC arrangement for MAC transmissions. i ··· N } b2, , b2 , where N is the length of each source More explicitly, the turbo code based design proposed in [11] block [8], [17], [52], [68]. The source sequence {b1} is gen- for communicating over a benign AWGN channel would erated by an equiprobable binary symmetric i.i.d. source, suffers from an error floor, when communicating over hostile { } i = i ⊕ ⊕ while b2 can be defined as: b2 b1 ei, where is Rayleigh fading channels. This makes the system less suitable the modulo-2 addition operation and ei is an independent for wireless applications. Later, a modified LDPC code was binary random variable assuming the logical value 1 with proposed in [17] for mitigating the above-mentioned error a cross-over probability of pe and 0 with a probability of floor, but nonetheless, a substantial error floor persisted, (1 − pe). For example, when {b1} and {b2} have a correlation when the correlation between the sources was low. Recently, coefficient of ρ = 0.9 given the perfect knowledge of {b1}, an iterative joint-turbo equaliser and decoder scheme was {b2} may be interpreted as the BSC’s output signal which was conceived for transmission over a multi-path Rayleigh fading contaminated by the bit-flipping error events occurring with 4 multiple access channel in [48] and [54]. Both schemes have cross-over probability of pe = 0.1. achieved a near-SW/S performance. i i Both the random variables of b1 and b2 in the pair of bit Turbo Trellis-Coded Modulation (TTCM) [107] has a streams {b1} and {b2} may be assumed to be i.i.d. for the structure similar to that of the family of binary turbo bit index i, hence both sources emit equiprobable bits [54]. codes, where two identical parallel-concatenated Trellis- Consequently, the entropy of each source is unity, which Coded Modulation (TCM) schemes rather than conventional yields a conditional entropy of: codes are employed as component codes. The classic TTCM design was outlined in [107], based on the search for the H(pe) = H(b1|b2) best TCM component codes using the so-called ‘punctured’ 1 h 1 1 1 2 2 2 i = lim H (b1, ··· , bi , ··· bN )|(b1, ··· , bi , ··· bN ) , minimal distance criterion, in order to approach the capacity i→∞ i of the Additive White Gaussian Noise (AWGN) channel. (7) Against this background, the bandwidth-efficient TTCM where H(p ) = p log 1 + (1 − p )log 1 concept is incorporated into our DJSC design, result- e e 2 pe e 2 1−pe ing in the Distributed Joint Turbo-Trellis Coded Modula- is the entropy of the binary random variable and ei is tion (DJSTTCM) concept conceived for transmission over used for parametrising the side-information. Therefore, the a Rayleigh fading channel. The TTCM code advocated was achievable SW rate region is given by the following three designed for our DJSC scheme in order to improve the inequalities [54] attainable throughput by considering the joint design of our error correction code and modulation scheme, where the R1 ≥ H(pe), parity bits are absorbed without any bandwidth expansion R2 ≥ H(pe), by increasing the number of bits bits per modulated symbol. R1 + R2 ≥ 1 + H(pe), By contrast in separated channel codes, such as Turbo or ≥ H(b , b ). (8) LDPC codes, a bandwidth expansion would be imposed, 1 2 which is proportional to the code rate. We will demonstrate IV. DJSC-BASED PERFECT SIDE-INFORMATION that our scheme is capable of attaining a near-SW/S per- In this section we assume relying on the idealized simplifying formance for a wide range of correlation coefficients ρ. assumption of having perfect side-information in the DSC Additionally, we intrinsically amalgamated our DJSTTCM scenario of Fig. 4. Explicitly, the sequence {b } is transmitted scheme with a realistic cooperative scenario, where both 2 at the rate of R = H(b ), which is typically referred to as sources’ transmissions are supported by a Relay Node (RN). 2 2 ‘side-information’ in most contributions [9], [10], [105] albeit Explicitly, the RN transmits both users’ signals with the aid again, this information can also be interpreted as another of a powerful SuperPosition Modulation (SPM) technique, desired source signal, which was perfectly recovered. The which judiciously shares the transmit power between the pair sequence {b } can also be transmitted through a practical of correlated signals. We refer to this scheme as our Dis- 2 imperfect channel, in which case an encoder structure similar tributed Joint Source TTCM (DJSTTCM-SPM) regime. Both to that of the first source {b } has to be implemented. The the RN and the Destination Node (DN) invoke a powerful 1 correlated sequence {b } is then compressed to a rate of turbo-style DJSTTCM-based decoder explicitly designed for 1 R = H(b |b ) for the sake of approaching the Slepian-Wolf exploiting the correlation amongst the source signals. The 1 1 2 bound, namely point A of Fig. 7, in order to achieve the overall powerful semi-analytical EXIT charts tool is used for deter- rate of H(b , b ). mining the most appropriate number of iterations between 1 2 the constituent components of the decoder for the sake of 4 The higher the cross-over probability pe, the lower the correlation achieving an early decoding convergence. between the two sources as ρ = 1 − 2pe.

VOLUME 4, 2016 1949 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

FIGURE 15. Block diagram of the DJSTTCM system [49] communicating over fading channels. The sources b1 and b2 are assumed to be correlated, i.e. we have H(b1|b2) 6= H(b1), and L(·) denotes the Logarithmic-Likelihood Ratios (LLR). The DJSTTCM decoder is further illustrate in Fig. 16.

We commence by describing the system model further punctured in order to achieve an increased compres- in Sec. IV-A, while the non-binary Maximum A-Posteri- sion ratio. The resultant bits are then mapped to BPSK sym- ori (MAP) decoding algorithm is modified in Sec. IV-B in bols, i.e. the modulation mode has been changed from QPSK order to exploit the side-information available at the receiver. to BPSK (QPSK/BPSK). Thus, the corresponding effective 0 The benefits of the side-information will be demonstrated by throughput is given by R = Rcm · Rp · log2(2) = 1 Bit Per our Bit Error Ratio (BER) results in Sec. IV-C, while the rate Symbol (BPS). Note that the SNR can be calculated in dB 0 regions of our schemes will be analysed in Sec. IV-D, where as SNR(dB) = Eb/N0(dB) + 10log10(R ). Then the modu- the SW/S bounds will be evaluated. lated symbol sequence {x1} is transmitted over an uncorrelated Rayleigh fading channel and the received symbol y1 is A. SYSTEM MODEL given by: The block diagram of the relying on perfect side-information y1 = hx1 + n, (10) DJSTTCM scheme [49] considered for transmitting correlated sources is illustrated in Fig. 15, where L(·) denotes the where h is the channel’s fading coefficient and n is the AWGN Logarithmic-Likelihood Ratios (LLR) of the bits. As shown having a variance of N0/2 per dimension. Therefore, the channel information probability of receiving y given x was in Fig. 15, the input sequence {b1} is fed into a TTCM 1 1 = m transmitted, gleaned from the soft demapper can be expressed encoder, which has a coding rate of Rcm m+1 and invokes a M = 2m+1-level modulation scheme. The TTCM encoded as [108]:  2  bits are then punctured at a rate of Rp. The resultant bit − (m) 0 1 y1 hx1 sequence c is then mapped to the corresponding modu- y | x(m) = − , 1 Pr( 1 1 ) exp   (11) lated symbols {x1}, before their transmission over uncorre- (πN0) N0 lated Rayleigh fading channel. Note that each specific symbol m ∈ { ··· M − } of the modulated symbol sequence, {x1}, is mapped using where 0, , 1 . µ(·)-QAM/PSK mapping function. The second bit sequence B. JOINT SOURCE-TTCM DECODER {b2} will be converted to the LLRs L(b2) = Le, which will be exploited as side-information. This conversion is necessary Our joint decoder is depicted in Fig. 16, where both because the joint decoder is a soft-decision-based one. These TCM decoders invoke the symbol-based MAP algorithm LLRs are characterised by the above-mentioned cross-over of [108] and [109] operating in the logarithmic-domain. Both probability pe and can be estimated as: TCM decoders are labelled with the round-bracketed indices, while the notation P, A and E represent the logarithmic prob- Pr(b1|b2 = +1) abilities of the parity, as well as a priori and of the extrinsic L(b1|b2) = ln Pr(b1|b2 = −1) information, respectively, where we have L(b2) = L(b2|b1) (m+1) (1 − p )Pr(b = +1) + p Pr(b = −1) of Eq. (9). The 2 -ary P1 probabilities, given in Eq. (11), = ln e 2 e 2 . (1 − p )Pr(b = −1) + p Pr(b = +1) associated with a specific (m + 1)-bit TTCM-coded symbol e 2 e 2 0 (9) c1 are fed into the TTCM MAP decoder. A pair of signal components are generated by the con- We assume that these LLRs are available at the destination stituent TCM decoders [108], [109] specifically, the extrinsic and to be exploited by the joint decoder. probability E is generated by each of the TCM decoders, As an example, we use a rate Rcm = 1/2 TTCM encoder while the a priori probability A is gleaned by each TCM relying on a puncturer of rate Rp = 2/1, which punctures one decoder from the other one. Furthermore, as seen in Fig. 16 bit out of two encoded bits. We assume that all the systematic the additional extrinsic probability, E2, extracted from the bits are punctured, while all the parity bits are transmitted to side-information {b2} is also added to the a priori prob- (1,2) (2,1) the decoder. However, the parity bit sequence may also be ability A, yielding A = [E1] + E2. Each of the

1950 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

−1 FIGURE 16. Block diagram of the DJSTTCM decoder of the DJSTTCM scheme of Fig. 15, the notations πs and πs represent the symbol interleaver and deinterleaver, respectively, while the side-information L(b2) is converted using the relevant LLR-to-symbol probability conversion which is explained in further details in Appendix A. constituent TCM blocks of Fig. 16 calculates the A Posteriori Probabilities (APP) using the forward and backward recursion method.5 Upon recalling the TTCM decoding and from Eq. (10), we are now in the position to formulate the channel’s transition metric as:

2 ηi(s`, s) = ln exp − |yi − hixi| /N0 . (12)

Then, both the backward and forward recursion of [108] are invoked for calculating βi−1(s`) and αi(s) as follows:

* (1,2) αi(s) = max (αi−1(s`) + ηi(s`, s) + A ), (13) all s` * (1,2) βi−1(s`) = max (βi(s) + ηi(s`, s) + A ), (14) all s

* where max represents the Jacobian logarithm evaluating all FIGURE 17. BER versus SNR performance of the proposed variables in the logarithmic domain, with (s`, s) denoting the DJSTTCM-QPSK scheme of Fig. 15 for correlation coefficients of ` ρ = 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.1 when transmitting over transitions emerging from the previous state s to the present uncorrelated Rayleigh fading channels. The number of decoding state s [108]. iterations between the pair of TCM MAP Decoders of Fig. 16 is I = 8, while the simulation parameters are shown in Table 4 and the related results are summarised in Table 5. C. DECODING WITH SIDE-INFORMATION As expected, the DJSTTCM scheme proposed benefits from the perfect side-information gleaned from the second source, QPSK, 8PSK and 16QAM signals, respectively, for trans- as documented by the BER curves of Fig. 17, Fig. 18 and mission over uncorrelated Rayleigh fading channels. In this Fig. 19, when the coded sequences {c1} are mapped to section the coded sequence {c1} shown in Fig. 15 will exhibit no puncturing, since we first aim for investigating our 5Detailed descriptions can be found in [108, Sec. 14.3]. Note that we illustrate the MAP process in the logarithmic domain in order to render it scheme’s as a function of the side-information. Observe in the compatible with Fig. 16. three figures, that the BER performance improves upon

VOLUME 4, 2016 1951 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

TABLE 4. Simulation parameters for the DJSTTCM scheme of Fig. 15 employed for quantifying the results of Fig. 17, Fig. 18 and Fig. 19.

FIGURE 18. BER versus SNR performance of the proposed DJSTTCM-8PSK scheme of Fig. 15 for correlation coefficients of ρ = {0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.1} when transmitting over uncorrelated Rayleigh fading channels. The number of decoding iterations between the pair of TCM TABLE 5. System performance of the DJSTTCM scheme of Fig. 15, when MAP decoders of Fig. 16 is I = 8, while the simulation parameters are the simulation parameters of Table 4 are used. The results are extracted shown in Table 4 and the related results are summarised in Table 5. from Fig. 17, Fig. 18 and Fig. 19 and contrasted to the corresponding separate decoding-based benchmark at BER= 10−5, respectively.

FIGURE 19. BER versus SNR performance of the proposed DJSTTCM-16QAM scheme of Fig. 15 for correlation coefficients of ρ = 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.1 when transmitting over uncorrelated Rayleigh fading channels. The number of decoding iterations between the pair of TCM MAP decoders of Fig. 16 is I = 8, while the simulation parameters are shown in Table 4 and the related results are summarised in Table 5. increasing the correlation coefficient ρ, where the corresponding simulation parameters are listed in Table 4.6 More explicitly, our proposed QPSK based DJSTTCM based schemes of Fig. 18 and Fig. 19, respectively. Thus, scheme has a significant gain of 5.6 dB over its counterpart- our proposed joint processing-aided scheme exhibits a bene- relying on separate-rather than joint decoding at a BER level ficial correlation exploitation capability, where the achievable −5 of 10 at correlation coefficient of value ρ = 0.9 associated gains are summarised in Table 5 with 010−5 representing the −5 with the BSC cross-over probability of pe = 0.05. However, SNR required for approaching a BER level of 10 . for a low correlation of ρ = 0.1 only a marginal gain of 1.3 dB can be attained over the above-mentioned benchmark D. RATE REGION DESIGN AND ANALYSIS at a similar BER level of 10−5. This is not unexpected, In a noisy environment, the rate region bound defined since the sources {b1} and {b2} are only loosely correlated. in Eq. (8) can be rewritten as [8], [11], [17], [54]: Similar trends can be observed for the BER curves corre- C1 C2 1 sponding to the DJSTTCM-8PSK and DJSTTCM-16QAM H(b1, b2) ≤ 0 + 0 ≤ 0 E log2(1 + γ1) R1 R2 R1 6 1 Again, the higher the cross-over probability pe, the lower the correlation + 0 E log2(1 + γ2) , (15) between the two sources as ρ = 1 − 2pe. R2

1952 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

where C1 = E log2(1 + γ1) and C2 = E log2(1 + γ2) denote the ergodic channel capacities between each of the sources and the destination, while γ1 and γ2 denote the corresponding received SNRs. In our system relying on perfect side-information we assume that {b2} is transmitted at R2 = H(b2) = 1, while we aim for compressing {b1} to its minimum rate, namely to R1 = H(b1|b2). Then, based on Eq. (15), the effective throughput of our scheme for the { } = 0 · | b1 link can be expressed as ηSW R1 H(b1 b2), while the SW/S bound is calculated as [48]: 0 R1 · H(b1|b2) ≤ C1, (16) where C1 represents the ergodic capacity of the uncorrelated Rayleigh fading channel. First we characterise the BER performance of our FIGURE 21. BER versus SNR performance of the proposed DJSTTCM-QPSK/BPSK scheme employing a range of DJSTTCM-QPSK/BPSK scheme of Fig. 15 for correlation coefficient correlation coefﬁcients ρ = {0.93, 0.9, 0.8, 0.7, 0.6}. of ρ = 0.9 when transmitting over uncorrelated Rayleigh fading channels. The number of decoding iterations between the pair of We opted for using 1/2-rate TTCM for encoding a block of TCM MAP decoders of Fig. 16 are I = 2, 4, 8, 12, 16 , and we apply NS = 12 000 symbols, resulting in Nb = 24 000 bits before puncturing rate of Rp = 2/1, while the other simulation parameters we remove all of the systematic bits from the TTCM coded are shown in Table 4. sequence with the aid of puncturing. The BER versus SNR performance of the proposed system is illustrated in Fig. 20.

FIGURE 22. DCMC and CCMC capacity curves when transmitting BPSK symbols over uncorrelated Rayleigh fading channels, here the curves were computed based on [110].

FIGURE 20. BER versus SNR performance of the proposed DJSTTCM-QPSK/BPSK scheme of Fig. 15 for correlation coefficients of ρ = 0.93, 0.9, 0.8, 0.7, 0.6 when transmitting over uncorrelated compressing the source sequence {b1}. Note in Fig. 20 Rayleigh fading channels. Note that, we apply puncturing rate of that all distributed schemes outperform the conventional Rp = 2/1, while the other simulation parameters are listed in Table 4 and the related results are summarised in Table 6. TTCM-QPSK benchmark scheme dispensing with joint decoding, which is labelled by the diamond markers, regard- The minimum SNR, 0lim, required for approaching less of the correlation coefﬁcient ρ, except for the very low the SW/S bound can be inferred from Fig. 22, which correlation scenarios of ρ = {0.7, 0.6}. More explicitly, at shows both the Continuous-input Continuous-output Mem- a BER = 10−5 the proposed DJSTTCM has an SNR gain oryless Channels (CCMC) capacity and the corresponding of 7.1 dB, 5.75 dB and 2.75 dB for ρ = 0.93, ρ = 0.9 BPSK based Discrete-input Continuous-output Memoryless and ρ = 0.8, respectively. However, as expected, with low Channel’s (DCMC) capacity curves. For example, when aim- correlation values the proposed scheme has an SNR loss of ing for a target throughput of ηSW = 0.469 BPS for our 1.7 dB and 3.6 dB, namely when we have ρ = 0.7 and DJSTTCM-QPSK/BPSK scheme, the DCMC curve indicates ρ = 0.6, respectively. Again, this is not unexpected, because requiring an minimum SNR of 0lim = −1.75 dB, as illus- for lower correlation cases the sources may be deemed to be trated in Fig. 22. Note that 0lim is represented with the aid of uncorrelated and hence they in fact provide, mis-information, = 0 · | vertical lines in Fig. 20, while again ηSW R1 H(b1 b2). misleading the joint decoder. It may be readily observed from As expected, the proposed scheme beneﬁts from the avail- Fig. 20 that at BER= 10−5 the scheme having ρ = 0.93 ability of perfect side-information constituted by {b2}, while has the minimum distance with respect to the SW/S limit,

VOLUME 4, 2016 1953 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

TABLE 6. System performance of the proposed DJSTTCM-QPSK/BPSK scheme of Fig. 15 when the puncturing rate is Rp = 2/1 and simulation parameters of Table 4 are used. The results are extracted from Fig. 20 and Fig. 23 when aiming for BER level of = 10−5.

throughput is only 0.14 bits away from the compression bound seen in Fig. 20. Table 6 summarized the performance of the proposed scheme.

V. DJSC-BASED SUPERPOSITION MODULATED RELAYING Sec. IV, has discussed and analysed a sophisticated relying on perfect side-information DJSC architecture [49], in which the second source sequence, relied upon as the side-information {b2} is assumed to be perfectly known at the receiver. However, this idealised simplifying assumption is impracti- cal, since in real-based applications the availability of error- free side-information cannot be ascertained. In this section we will relinquish this idealised assumption, explicitly both sources are TTCM encoded and then compressed before transmission through a Rayleigh fading Multiple Access Channel (MAC). Additionally, both sources are supported

FIGURE 23. Theoretical SW bound as well the rates (R1, R2) achieved by by a SPM-based RN which judiciously allocates the trans- the proposed DJSTTCM-QPSK/BPSK scheme of Fig. 15 for different pe mit power between the pair correlated signal, resulting in values, where 0 denotes the SNR required for achieving 10−5 DJSTTCM-SPM. The proposed cooperative system model a BER = 10−5. is described in Sec. V-A, while the Phase-I encoder and decoder as well as our rate region analysis will be discussed in Sec. V-B. Then a brief discussion concerning the SPM i.e. we have 010−5 −0lim = (−3.5)−(−6.5) = 2.0 dB, while the scheme associated with ρ = 0.6 has a 4.25 dB distance design employed in Phase-II transmission will be presented from the limit.7 in Sec. V-C, followed by the corresponding analysis of our The effect of the number of iterations I between the TCM results in Sec. V-D. decoders of Fig. 16, on the overall DJSTTCM-QPSK/BPSK scheme’s performance is illustrated by Fig. 21. It can be A. SYSTEM MODEL observed that doubling the number of iterations from I = 2 Let us now first take a quick look into the cooperative to I = 4 will improve the scheme’s performance by 1.5 dB, communications scheme, which constitutes an effective tech- while doubling the complexity further will only enhance the nique of supporting users either with objective of combating system’s performance by 0.5 dB. Furthermore, doubling the the channel fading or enhancing the overall transmission complexity beyond I = 8 would not provide any further gain, throughput [64]–[66]. Consider the cooperative scheme por- despite further increasing the decoding complexity. Hence we trayed in Fig. 24, where the pair of Source Nodes (SNs) invoke I = 8 iterations in our decoder. transmit their information to the RN during the first time The SW theoretical bound and the achievable rates slot (Phase-I). Then, the RN retransmits the information obtained for the proposed DJTTCM-QPSK/BPSK schemes during the second time slot (Phase-II). Over the years a are shown, respectively, in Fig. 23. The rates achieved cor- large variety of protocols have been designed for processing − respond to a BER of 10 5 and on average the system’s the SNs’ transmitted signals [64]–[66], [113]. In general, these protocols can be classified into fixed relaying and 7It is possible to further reduce the gap to capacity by using irregular adaptive relaying [66]. In the former family, the available code designs [111], [112] at the cost of a higher decoding complexity, and a high interleaver length, i.e. latency, at the cost of precluding inter-active communication resources, of time, frequency, space, trans- lip-synchronised video communication. mitted power etc., are divided between the SNs and RNs in

1954 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

dUR = dRD = dUD/2, hence GUR = GRD ≈ 6.02 dB. It is convenient for our discussions to deﬁne the term referred to as transmit SNR as the ratio of the power transmitted from node a to the noise power experienced at the receiver of node b as8: 2 E |xa| 1 SNRt = = . (18) N0 N0 Thus, we arrive at:

SNRr = SNRt Gab

0R = 0T + 10log10(Gab) [dB], (19)

where we have 0R = 10 log10(SNRr ) and 0T = 10 log10(SNRt ). FIGURE 24. Schematic diagram of the DJSC-aided RN-assisted SPM of Similar to the source correlation model illustrated in Fig. 34, where d is the geographical distance between the UD Sec. III, the BSC philosophy is used for modelling nodes U1,2 and DN. the correlation between the source sequences {b1} = { 1 2 ··· i ··· N } { } = { 1 2 ··· i ··· b1, b1, , b1, , b1 and b2 b2, b2, , b2, , N } a time-invariant fashion. By contrast, in the latter schemes, b2 , where N is the length of each source block. More explic- as suggested by the terminology, these resources will be itly, the source sequence {b1} is generated by an equiprobable shared adaptively in sophisticated ways [66], [113]. Then, binary symmetric i.i.d. source, while {b2} can be formulated i = i ⊕ ⊕ according to how the RN would deal with its received signals, as b1 b2 ei, where is the modulo-2 addition operation each relaying scheme might be further categorised into four and ei is an independent binary random variable assuming the main classes, namely the Amplify-and-Forward (AF) [114], logical value 1 with a cross-over probability of pe and 0 with Decode-and-Forward (DF) [115], [116], Compress-and- a probability of (1 − pe). Forward (CF) [117] and Coded Cooperation [118] protocols. Let us now embark on the design of a joint source-channel Let us again, consider the schematic of Fig. 24, where encoding/decoding scheme for the RN and DN. {b1} and {b2} are pair of correlated binary information sequences at the SNs, where one (both) of them has (have) B. FIRST TIME SLOT (PHASE-I) to be compressed before their transmission to the RN. More The basic block diagram of the DJSTTCM-SPM scheme is explicitly, the encoders of both the source nodes U1 and U2 shown in Fig. 25, which relies on the Phase-I and Phase-II have to encode and then compress {b1} and {b2} indepen- transitions during the first and second timeslots, respectively. dently of each other. In other words, neither the source’s Our system can be viewed as a two-stage serially concate- observations from the other source nor the correlation coef- nated structure. Explicitly, in the first timeslot, the pair of ficient are known by one of the SNs concerning the other. correlated sequences, {b1} and {b2}, are encoded by the However, the RN is capable of reconstructing both sequences powerful TTCM encoders, or ‘‘outer encoders’’, where each { } { } = m m+1 through exploiting the correlation between b2 and b1 [8]. has a coding rate of Rcm m+1 and invokes a 2 -level The schematic of our proposed single-relay-aided cooper- modulation scheme. Note that the second user stream {b2} ative model is shown in Fig. 24, where both SNs, namely is separated by a user-specific bit-interleaver πb from {b1} U1 and U2 have a single antenna each. They transmit their in order to exploit the user correlations via the inner itera- correlated information signals to the Destination Node (DN) tion (Iin) that is between the two TTCM decoders at the RN with the aid of a twin-antenna-aided RN. The communication and DN, as illustrated in Fig. 26. Then both TTCM-encoded paths shown in Fig. 24 are subject to both path-loss as well sequences, namely {c1} and {c2} will be interleaved aiming as to uncorrelated Rayleigh fading. Assuming a free-space for facilitating iterative information exchange between the path-loss exponent of α = 2, the corresponding reduced- TTCM decoder and the Multi-User Detector (MUD), which pathloss-induced geometrical gain experienced by the we refer to as the outer iteration (Iout). Here, the symbol- Sources-to-Relay (SR) link and Relay-to Destination (RD) based interleavers, namely π1 and π2, are invoked for intro- link with respect to the Source-to-Destination (SD) link may ducing time-diversity by scrambling the codeword sequences. be calculated, respectively, as [119], [120]: As a consequence, this would provide much-needed indepen- 2 2 dent a priori information at the output of the outer decoder, dUD dUD GUR = ; GRD = , (17) when aiming for combating the deleterious effect of channel dUR dRD fading [108], [121]. Next, the TTCM-interleaved coded bit where dUD denotes the distance between the source nodes 8However, the concept of transmit SNR [120] is unconventional, as it U1, U2 and the DN. In our model the RN is situated exactly relates quantities to each other at two physically different locations, namely at the mid-point between the SNs and DN. Thus, we have the transmit power to the noise power at the receiver.

VOLUME 4, 2016 1955 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

FIGURE 25. Block diagram of the DJSTTCM-SPM (Phase-I and Phase-II), when communicating over Rayleigh fading channels. The DJSTTCM decoder is further illustrated in Fig. 26.

0 0 sequences c1 and c2 are punctured at a rate of Rp, before they are mapped to the corresponding modulated symbols {x1} and {x2} using the mappers of Fig. 25, for transmission over an uncorrelated Rayleigh fading MAC. Each speciﬁc symbol of both modulated symbol sequences is mapped using QAM/PSK mapping function. Phase-I transmission from the L = 2 SNs (U1 and U2) to the P = 2-antenna based RN, might be interpreted as a Space-Division Multiple Access (SDMA) scenario [108]. Hence, when each user invokes M 0-ary PSK-or-QAM, the signal received at the RN can be written as:

y = Hx + n, (20)

T T where y = [y0, y1, ··· , yP−1] and n = [n0, n1, ··· , nP−1] are (P × 1)-dimensional vectors that represent the Phase-I received signals and noise vectors, respectively. Note that FIGURE 26. Schematic of the DJSTTCM decoder employed at the RN and each element in n represents the complex-value of AWGN DN of the DJSTTCM-SPM scheme of Fig. 24, the notation L(·) denotes the having a variance of N0/2 per dimension. Additionally, the LLR sequences, and the superscript a, e and o denote a priori, extrinsic channel is represented by the (P × L)-element matrix H, and a posteriori nature of the LLR, respectively. A(·) and E(·) represent the a priori and extrinsic probabilities, and the notations π and π−1 = ··· T i i while the transmitted signal x [x0, x1, , xL−1] is represent the symbol-based interleaver and deinterleaver for i th user, an (L × 1)-element vector. Assuming perfectly synchronised respectively, while π and π−1 denotes the bit-based interleaver and b b 0L deinterleaver. transmission between U1 and U2, there are M = M possible phasor combinations for the transmitted signal vector x. of the MAP algorithm, similar to Eqs. (12), (13) and (14), 1) JOINT SOURCE-TTCM DECODER respectively.9 Accordingly, the a posteriori probabilities of As the decoder schematic of Fig. 26 shows, during I , the in the uncoded information gleaned from both of the TTCM decoding process of {b } at the output of ‘‘TTCM Dec ’’, 1 1 decoders, will be converted to LLRs L (b ) and L (b ) during would utilise the LLR estimate corresponding to {b }, namely o 1 o 2 2 the I . L (b ) extracted from ‘‘TTCM Dec ’’, which is also referred in e 2 2 Thus, the employment of turbo-like parallel architectures to as the side-information. Likewise, the decoding of {b } 2 would be appropriate in this context for approaching the the- requires the LLR of {b }, namely L (b ). Note that, each 1 e 1 oretical performance limits [108], which efﬁciently exploits TTCM decoder employs a symbol-based MAP algorithm, the source-correlation, as documented in [8], [11], and [54]. where the side-information LLRs will be converted to symbol probabilities and then incorporated in the channel’s transition 9The probability-to-LLRs as well as LLRs-to-probability conversions are metric as well as in the backward and forward recursion illustrated in Appendix A.

1956 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

0 0 Hence, at the RN the estimated information sequences, bbr,1 where M = 4 and i ∈ {0, ··· , M − 1}. Based on Eq. (22) and bbr,2 are determined by exchanging extrinsic information and Eq. (23), the channel probabilities feed into the pair of in a parallel manner between the constituent decoders and the TTCM decoders at the RN can be expressed using: MUD. (i) | = | = (i) × (i) First, the MUD detects the received signal using the robust, Pr(x1 y) Pr(y x1 x1 ) Pr(x1 ), (24) but potentially complex ML detector that aims for choosing (i) | = | = (i) × (i) Pr(x2 y) Pr(y x2 x2 ) Pr(x2 ), (25) the specific received symbol x that maximise the received signal probability. The probability of the receiving vector y (i) = (i) where Pr(x1 ) Pr(x2 ) are all equiprobable probabilities conditioned on the transmission of x(r), where each symbol of 1/M 0 during the first outer iteration. Additionally, for the in x might assume r ∈ {0, ··· , M − 1} possibilities is char- (i) = case when there is no outer iteration, we have Pr(x1,2) acterised by [108]: (i) · Pr(c1,2) due to the one-to-one mapping µ( ) function used. 2 ! However, for further outer iterations, i.e. when I > 1, 1 y − Hx(r) out | (r) = − the Pr(c(i) ) signify the a priori probabilities of the code- Pr(y x ) P exp , (21) 1,2 (πN0) N0 0 words A(c1,2) which are the feedbacks gleaned from the k k pair of the TTCM decoders to the MUD, as Fig. 26 illus- where (.) denotes the Frobenius norm of the vector (.). (i) trated. Therefore, the a priori probabilities Pr(c1,2) will no longer be equiprobable, which results in decoding perfor- TABLE 7. Table of all possible combinations, where both x1 and x2 uses QPSK-based Set-Partition labelled mapping. mance enhancement. Next,the MUD estimates the extrinsic 0 probabilities E(c1,2) that are forwarded, after applying the appropriate de-interleavers, to the TTCM decoders for com- pleting the outer iteration Iout, as illustrated in Fig. 26. Both TTCM decoders invoke a symbol-based MAP algorithm that is detailed in [108]. Each decoder will first estimate the a posteriori probabilities related to the uncoded information bits. These probabilities will be converted into LLRs, namely Lo(b1) and Lo(b2), which are then updated and appropriately de/interleaved to generate the a priori LLRs, La(b1) and La(b2), as shown in Fig. 26. These LLRs are then exchanged between the two TTCM decoders through the Iin in order to exploit the correlation knowledge between the two users U1 and U2. However, during the Iin process the LLRs have to be updated in order to avoid the error propagation using the BSC cross-over probability pe, as follows [14], [17]:

(1 − pe)exp[Le(b1,2)] + pe U(Le(b1,2)) = ln , (26) (1 − pe) + peexp[Le(b1,2)] where U is the updating function shown in Fig. 26. Moreover, the BSC’s cross-over probability pe can be estimated by comparing the reliable extrinsic LLR gleaned from each decoder, namely Le(b1) and Le(b2) as [17]:

1 N exp[L (b )] + exp[L (b )] = X e 1,i e 2,i In our Phase-I transmission each user employs QPSK bpe . (27) N 1 + exp[Le(b1,i)] 1 + exp[Le(b2,i)] scheme, hence we have M = 42 = 16 possible transmitted i=1 phasor combinations that are deﬁned explicitly in Table 7. 2) DECODING WITH SIDE-INFORMATION Thus, given the combinations shown in Table 7, the channel In this section, we will evaluate the performance of our information probabilities of receiving y given that x and x 1 2 joint decoder using the estimated side-information during the were transmitted can be extracted from the M = 16-ary set Phase-I transmission of Fig. 25. Here we opted for employ- of probabilities of Eq. (36), respectively, as: ing the powerful semi-analytical EXIT charts technique for M0−1 analysing the convergence behaviour of the joint decoder. The 0 | = (i) = X | (i+(M ×j)) = (i) Pr(y x1 x1 ) Pr y x x1 , (22) EXIT curves of the outer DJSTTCM decoder recorded for j=0 various correlation values of ρ = {0.9, 0.8, 0.6, 0.4, 0.2, 0.1} M0−1 are shown in Fig. 27, where the related simulation parameters 0 | = (i) = X | (j+(M ×i)) = (i) Pr(y x2 x2 ) Pr y x x2 , (23) are tabulated in Table 8. Note that here we do not perform any j=0 puncturing in any of the coded bit sequences.

VOLUME 4, 2016 1957 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

TABLE 8. Simulation parameters for the Phase-I transmission of the schematic of Fig. 25.

3) RATE REGION DESIGN AND ANALYSIS As stated in Sec. II-C, the source/channel separation is not optimal for our Phase-I transmission [8], [51]. Nonetheless, the theoretical limit that we will consider in our work assumes source/channel separation. Giving this assumption, the limit of reliable communication for correlated sources may be deﬁned using Eq. (8). By contrast, the CCMC capacity of each phase of the scheme shown in Fig. 25 for transmission over fading channels, when invoking the SDMA scheme can be deﬁned as [122]: H HQx H C = E log2 det IN + , (28) N0

where E denotes the expectation operation and Qx is the covariance matrix of the transmitted vectors, while HH is the Hermitian transpose of the channel matrix. Note that effective transmission rate of Phase-I is given by: 0 R = Rp · Rcm · log2(M) · L, (29) 0 where SNR(dB)= Eb/N0(dB) + 10log10(R ) and L denotes FIGURE 27. EXIT curves of the outer decoder of the DJSTTCM scheme seen in Fig. 26 for the correlation coefficients of ρ = {0.9, 0.8, 0.6, 0.4, the number of transmit antennas. Thus, the overall Phase-I 0.2, 0.1}, where we have Iin = 4. All parameters are listed in Table 8. transmission capacity can be expressed from Eq. (8) and Eq. (28) as: These EXIT curves characterise the relationship between 1 HQ HH ≤ + x the a priori input, A(c1) and the extrinsic output, E(c1), of H(b1, b2) 0 E log2 det IN , (30) R N0 the TTCM-Dec1 shown in Fig. 26, while the number of inner iterations is ﬁxed to (Iin = 4). Thus, the EXIT characteristics assuming an equal power allocation, where U1 and U2 trans- of the outer decoder are independent of SNR. As expected, mit at the same power. The corresponding effective through- 0 the higher the correlation, the faster the convergence upon put of a single source is given by ηSW = 1/2 · R · H(b1, b2). increasing IA(c1) where the area above the outer decoder’s The above CCMC capacity assumes having an optimally- EXIT curve is higher for larger values of correlation coefﬁ- distributed/continuous-amplitude input signal, in which the cients ρ. This rapid converge will facilitate having an open capacity is only bounded by the power transmitted as well EXIT tunnel for lower SNR values, hence saving a signif- as by the bandwidth allocated [122]. Hence, the employment icant amount of transmit energy, as it will be illustrated of the DCMC capacity is more accurate in our DJSTTCM in Sec. V-B.3. scheme design, since the bound considers both the effects

1958 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

of having discrete inputs as well as specifics of practical non-Gaussian distributed transmit signal of realistic digital modulation schemes. The DCMC capacity can be expressed from [110] as: M−1 Z ∞ Z ∞ X r r CDCMC = max ··· p(y | x )p(x ) p(x0···xM−1) −∞ −∞ r=0 p(y | xr ) · log dy [bit/sym], (31) 2 p(y) where symbol definitions of Eq. (20) and Eq. (21) are still valid. Furthermore, Eq. (31) can be be simplified for M-ary phasor combinations as follows [110]:

M−1 " M−1 # 1 X X C = log (M) − E log exp(9r ) DCMC 2 M 2 i r=0 i=0 [bit/sym], (32) where we have: P−1 r 2 2 X − yi − hix + ni + |ni| r FIGURE 28. EXIT curves that characterise DJSTTCM-QPSK scheme for 9i = , (33) N correlation coefficients of ρ = 0.8, 0.2 when transmitting over = 0 i 0 uncorrelated Rayleigh fading MAC for Phase-I transmission. where again, P is the number of receive antennas at the RN. Table 8 summarises the main simulation parameters. The EXIT chart of Fig. 28 characterises our iterative joint decoder, when the transmit SNR of 0.15 dB and 2.6 dB are invoked along with the source correlations of ρ = 0.8 and ρ = 0.2, respectively.10 All the other simulation parameters are listed in Table 8. Specifically, Fig. 28 suggests that four inner iterations ‘‘Iin = 4’’ between the outer decoder constituted by the pair of TTCM decoders of Fig. 26 will facilitate an open EXIT tunnel for both correlation values of ρ = {0.8, 0.2}. Hence, as infinitesimally low BER can be achieved at the same level of the transmit SNR. Nevertheless, reducing the number inner iterations to ‘‘Iin = 2’’ would result in a closed EXIT tunnel hence leading to a residual BER. More explicitly, as seen in Fig. 28, increasing the number inner iterations to ‘‘Iin = 6’’ would not results in any noticeable performance gain, despite increasing the decoding complexity. For the case of achieving an open EXIT tunnel and for the trajectories to reach the right-hand axis, a transmit FIGURE 29. BER versus SNR performance of the proposed DJSTTCM-QPSK scheme of Fig. 25 for correlation coefficients of ρ = 0.8, 0.6, 0.4, 0.2 , SNR of 0.15 dB and 2.6 dB is needed for ρ = 0.8 and when transmitting over uncorrelated Rayleigh fading MAC during the ρ = 0.2, respectively, as shown in Fig. 28. Additionally, four Phase-I transmission. Table 8 summarises the main simulation outer iterations ‘‘I = 4’’ between the MUD the pair of parameters. The related results are summarised in Table 9, while the SNR out limits values 0lim are extracted from the DCMC capacity curves of Fig. 30. TTCM decoders is required as illustrated, in the trajectories of the same figure. The Bit Error Ratio (BER) results depicted in Fig. 29 support the prediction documented by the EXIT coding scheme for a block of 12 000 symbols for both users charts of Fig. 28. and transmitted a total of 4000 blocks. Table 8 summarised We first characterise the BER performance of DJSTTCM the rest of the parameters. The attainable BER versus SNR when QPSK modulation is employed for ρ = {0.8, 0.6, 0.4, performance is depicted in Fig. 29, where the SNR is given 0.2}. Here, we opted for invoking 1/2-rate TTCM as a channel 0 by SNR(dB) = Eb/N0(dB)+10log10(R ), where the effective 0 10Although the extrinsic Mutual Information (MI) transfer characteristics throughput in this case R = Rcm · Rp · log2(M) · L = 1/2 · of the inner and outer components intersect at a point below the (1, 1) point, 1 · 2 · 2 = 2 BPS. As portrayed in Fig. 29, our proposed a low BER is still attainable as shown [121], which is verified by Fig 29. scheme outperformed the conventional TTCM-QPSK bench- It is possible to approach the (1, 1) point that is linked to a steep turbo-cliff, at the cost of a higher decoding complexity, via concatenating the MUD inner mark dispensing with joint decoding, when communicating demapper with a recursive decoder component [123]. over the 2 × 2 MAC considered. Note that our benchmark

VOLUME 4, 2016 1959 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

scheme is represented by the filled diamonds. As expected, Iin = 1 in Fig. 31 would overlap. This is not unexpected, our distributed scheme benefits from the correlation among because the extrinsic LLRs Le(b1,2) are set to zero for the the two sources. To elaborate further, at a BER level of first iteration. Thus, we opted for ‘‘Iin = 4’’ and ‘‘Iout = 4’’ −5 10 the proposed scheme associated with ‘‘Iin = 4’’ and in our simulations. ‘‘Iout = 4’’ has an SNR gain of 3.8 dB, 2.8 dB, 2.05 dB and 1.4 dB for ρ = {0.8, 0.6, 0.4, 0.2}, respectively.

FIGURE 31. BER versus SNR performance of the proposed DJSTTCM-QPSK scheme of Fig. 25 for correlation coefficients of ρ = 0.8, 0.6, 0.4, 0.2 when communicating over uncorrelated FIGURE 30. DCMC and CCMC capacity curves of 2 × 2 MAC for Rayleigh fading MAC for Phase-I transmission. Table 8 summarises uncorrelated Rayleigh fading, where the curves were computed the main simulation parameters. based on [110]. The vertical lines correspond to the SNR limits 0lim that are plotted in Fig. 29. The rate region based on the SW theoretical bound as well as the achievable rates are presented in Fig. 32. Similar to the In order to evaluate our system’s performance, we have to SW/S limit, 0 , the minimum achievable rates η −5 of our estimate the minimum SNR, 0 , required for approaching lim 10 lim scheme can be evaluated as follows: the SW/S bound. More explicitly, the 0lim values are obtained from the DCMC capacity shown in Fig. 30. The CCMC • First, the SNR values capable of achieving a BER level −5 capacity curve is also shown in Fig. 30 for comparison. More of 10 or better will be recorded. specifically, we invoke DJSTTCM associated with ρ = 0.8, • Next these SNRs will be linked back to the effective where the maximum overall achievable throughput is throughput, η10−5 , using the DCMC capacity curves of 0 Fig. 30. ηSW = 1/2 · R · H(b1, b2) = 1.469 BPS. The DCMC capacity curve suggests that the minimum required SNR Recall that, we assume that both U1 and U2 have a sim- corresponding to ηSW = 1.469 BPS is 0lim = −0.7 dB, ilar coding and transmission rate, hence they have similar as shown in Fig. 30. Similarly, the 0lim values of the related maximum achievable rates. Our proposed scheme is capable schemes associated with different correlation coefficients are of operating within 0.12 bits from the SW rate region for inferred from the DCMC curves, explicitly, they are indicated ρ = {0.8, 0.6, 0.4, 0.2}, as depicted in Fig. 32. Specifically, with the aid of vertical lines in Fig. 29. At BER = 10−5 the Phase-I transmission performance is summarised at a the scheme having the highest correlation of ρ = 0.8 has glance in Table. 9. For further visualization, Fig. 33 illustrates the minimum distance from the SW/S limit, as readily seen both the rate region as well as the achievable compression from Fig. 29. More explicitly, we have 0 − 0lim = (0.15) − rates of our proposed scheme in a 3D diagram. (−0.7) = 0.55 dB, while the scheme associated with the lowest correlation of ρ = 0.2 operates within 1.1 dB of the C. SECOND TIME SLOT (PHASE-II) bound. In Sec. V-B we have evaluated our DJSTTCM scheme’s Moreover, the effect of increasing the number of outer Phase-I performance for a MAC scenario, but without iterations between the joint TTCM decoders and the MUD, employing a real puncturing in any of the coded sequences, 0 0 = denoted as Iout in Fig. 26, is outlined in Fig. 29. Increasing namely in c1 and c2 of Fig. 25, i.e. we had Rp 1. the number of iterations from ‘‘Iout = 1’’ to ‘‘Iout = 4’’ will However, later in Sec. V-D, one of those coded sequences enhance the system’s performance by about 0.75 dB. It is will experience real puncturing, leaving its modulated signal also worth mentioning that, more than one inner iterations, more susceptible to the effects of noise. Hence, as a remedy in Fig. 26 are required, in order to efficiently exploit the SPM has been invoked at the RN. Explicitly as the terminol- joint decoding design, as illustrated in Fig. 31. Employing ogy implies, we combine multiple independent bit/symbol a single Iin, will fail to exploit the signal correlation, hence streams of the users for forming a combined constellation, the BER curves recorded for all correlation coefficients using where the available protection resources might not equally

1960 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

−5 TABLE 9. Phase-I system performance of the DJSTTCM-QPSK of Fig. 25, where 0 and ηSW are documented at BER = 10 . Both 0lim and 0 are in dBs. The parameters of Table 8 are used.

FIGURE 33. Theoretical SW bound having the achievable rates R1 and R2 −5 of BER = 10 for ρ = 0.8, 0.6, 0.4, 0.2 corresponding to pe. The parameters of Table 8 are used.

1) RELAY-AIDED LOW ORDER SUPERPOSITION MODULATION The concept of cooperative transmission-aided SPM mapping FIGURE 32. Theoretical SW bound for each user rate R1, R2 attained was introduced in [125] and then it was further investigated using the DJSTTCM-QPSK scheme of Fig. 25 for Phase-I transmission for in [128] and [129]. In Phase-II, the RN will re-encode both different correlation coefficient values. The main simulation parameters ˆ ˆ are listed in Table 8, while the related results are summarised in Table 9. br,1 and br,2 using a pair of 1/2-rate TTCM encoders cor- (a) ρ = 0.80. (b) ρ = 0.60. (c) ρ = 0.40. (d) ρ = 0.20. responding to both users, respectively. As illustrated in the lower part of Fig. 25, the resultant QPSK modulated sig- distributed among the streams or users [124]. As a bene- nals xˆr,1 and xˆr,2 will be linearly combined to generate ﬁt, the total achievable rate of the entire scheme might be a 16QAM constellation xspm using the SPM technique as: enhanced, while keeping the complexity manageable. The resultant combined constellation will eliminate the need for = ˆ + ˆ extra extra transmit antennas or time slot or bandwidth and xspm r1xr,1 r2xr,2, (34) still accommodates the transmission of an extra stream or user [125], [126]. Albeit naturally of the cost of reducing the where the transmitted signal energy is normalized to unity, Euclidean distance amongst the constellation points, hence h i h i i.e. we have E xˆ2 = E xˆ2 = 1, while both SPM requiring an increased SNR. Both SPM and Hierarchical r,1 r,2 2 + 2 = Modulation (HM) can be considered as a member of the scaling factors have to satisfy r1 r2 1. To elabo- layered modulation family, where the former combines the rate further, the 16QAM scheme obeying Eq. (34) is shown symbols of different users, while the latter combines bits from in Fig. 34, where the weighting factors r1 and r2 determine the same bit streams.11 The next section will discuss the SPM which of the QPSK signals will be given a higher protection. that we invoke at our RN. Explicitly, when we have r1 > r2, then xr,1 has a higher protection, while xr,2 will become the less well protected 11HM has the ability to transmit multiple simultaneous data streams auxiliary signal. The minimum Euclidean distance d between treating them as different layers with different protection levels according to their priorities, where each of the different layers may be demodulated the 16QAM-SPM constellation points can be either d1 or d2, separately [127]. as shown in Fig. 34, which may be fully characterised using

VOLUME 4, 2016 1961 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

(i) = (i) where the Pr(xr,1) Pr(xr,2) are all equiprobable probabilities for the ﬁrst iteration. The DN employs a DJSTTCM decoder which was discussed in Sec. V-B.1.

FIGURE 34. 16QAM superimposed symbol constellation generated from a pair of QPSK-based modulated signals, where we assume that r1 > r2. r1 as [130]:  q q − 2 − − 2 ≥ min 2 1 r1 , 2(r1 1 r1 ) when(r1 r2) d = q − 2 − min 2r1, 2( 1 r1 r1) when(r1 < r2). (35)

In [130], the SPM weighting factors, r1 and r2, that maximise the minimum distance d were derived and the attainable performance was examined, where the optimum pair was FIGURE 35. EXIT curves of the DJSTTCM-aided 16QAM based SPM scheme of Fig. 34 based on the correlation coefficient of ρ = 0.4 for found to be (r1, r2) = (0.894, 0.447). Finally, the DN detects Phase-II transmission over uncorrelated Rayleigh fading channels. and estimates the received signal in a similar manner to that The simulation parameters are summarised in Table 10. at the RN, which was detailed in Sec. V-B.1. However, the MUD will recover probability of receiving yd given that Similar to the analysis used in Phase-I, we opted for 16QAM-SPM signal of Eq. (34) was transmitted using [130]: using the EXIT charts to visualise the information exchange between the DN’s constituent decoders. The simulation Pr(yd | xr,1, xr,2) parameters are tabulated in Table 10 and Fig. 35 shows that 2 ! 1 yd − h(r1xr,1 + r2xr,2) the layer that invokes the lower ratio of r1 = 0.447 will need = exp − , (36) a higher SNR of 10.5 dB in order to attain an open EXIT (πN0) N0 tunnel and vice versa. In other words, the QPSK signal xˆr,1 specifically, and with the aid of Fig. 34, the probabilities of will need nearly 4.0 dB less power to achieve a low BER, receiving yd given that xr,1 and xr,2 were transmitted can be when it is scaled with the aid of r1 = 0.894 compared extracted from Eq. (36), respectively, as: to xr,2 weighted by r1 = 0.447. Hence, using SPM of M0−1 Fig. 34 in Phase-II would equip our scheme with unequal + 0× | = (i) = X | (i (M j)) = (i) error protection capability that will be further investigated Pr(yd xspm xr,1) Pr yd xspm xr,1 , j=0 in Sec. V-D. In harmony with the Phase-I BER performance (37) of Fig. 29 discussed in Sec. V-B.3, the DJSTTCM-aided M0−1 + 0× 16QAM based SPM scheme has explicitly benefited from | = (i) = X | (j (M i)) = (i) Pr(yd xspm xr,2) Pr yd xspm xr,2 , the sources’ correlation after Phase-I decoding. Our joint j=0 (38) iterative scheme outperformed the system dispensing with joint decoding, as shown in Fig. 36, which was represented 0 −5 where we have M = log2 (M) = log2 (16) = 4, since we by the filled diamond. For example, at a BER level of 10 use 16QAM-SPM modulation scheme and i ∈ {0, ··· M 0−1}. and at ρ = 0.8 the proposed schemes associated with Thus, as shown in Fig. 34, our SPM considers the two least r1 = 0.894 and r2 = 0.477 outperform the benchmarker by significant bits for characterising xr,1, while the two most as much as 2.8 dB and 3.4 dB, respectively, as seen in Fig. 36. significant bits are mapped to xr,2. Based on Eq. (37) and Furthermore, as expected this gain is reduced, as the correla- Eq. (38) the probabilities that are provided to each of the tion diminishes, as detailed in Table 11. TTCM decoders at the DN can be expressed as: D. OVERALL SYSTEM PERFORMANCE RESULTS Pr(x(i) | y ) = Pr(y | x = x(i) ) × Pr(x(i) ), (39) r,1 d d spm r,1 r,1 In order to investigate our system in a more challenging (i) | = | = (i) × (i) Pr(xr,2 yd ) Pr(yd xspm xr,2) Pr(xr,2), (40) scenarios similar to Sec. IV, we apply puncturing to one

1962 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

TABLE 10. Simulation parameters for Phase-II transmission shown in the schematic of Fig. 25.

TABLE 11. Phase-II system performance of the DJSTTCM-16QAM based SPM scheme of Fig. 34 when compared to the TTCM-16QAM benchmark, where 0-benchmark 0 denotes the SNRs that correspond to a BER level of = 10−5. 10−5

= i.e. the puncturing rate is Rp2 2/1. As a result, all systematic bits of U2 are punctured, retaining only the parity bits for are transmission. However, the unequal protection nature of the SPM would allow us to beneﬁcially prioritise the protection of the sources. Two different cases that might link to two practical scenarios were investigated which are follows: • Case One: the punctured source U2 will be assigned the high SPM ratio of r2 = 0.884, which can be beneﬁcial, when the battery charge of U2 is limited. • Case Two: the punctured source U2 will be assigned the low SPM ratio of r2 = 0.447. This case is applicable in the scenario, when the source U1 has more valuable information, while U2 can be considered to provide less important side-information. FIGURE 36. BER versus SNR performance of the DJSTTCM-aided 16QAM based SPM scheme of Fig. 34 scheme for correlation coefficients of In our cooperative system simulations, the RN is located at ρ = 0.8, 0.6, 0.4, 0.2 for Phase-II transmission, where the simulation the mid-point between the SNs U1/U2 and the DN. Thus, from parameters are tabulated in Table 10. Eq. (17), we have GUR = GRD ≈ 6.02 dB, and accordingly, the received becomes SNRr = SNRt + 10log10(GUR/GUR). of the source user’s coded sequence. During the Phase-I Additionally, both the RN and DN decoders invoke ‘‘Iout = 4, transmission, similar to our previous design in Sec. IV, both Iin = 4’’ iterations. users will invoke the 1/2-rate TTCM code. However, the The EXIT curve of Fig. 37 illustrates that source U2 second user, U2 will apply puncturing to its coded sequence. requires a higher transmit power in order for the tunnel to be Explicitly, one of its pair of encoded bits is punctured, come open than the source U1 for the same SNR of 2.0 dB.

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punctured source U2 during Phase-II transmission. Explicitly, the overall performance of the non-punctured source U1 was found to be similar to its punctured counterpart, namely within approximately one dB. Fig. 38 shows the performance of our cooperative DJSTTCM-SPM scheme for both Case One and Case Two, when the side-information source U2 is assigned r2 = 0.894 and r2 = 0.447, respectively. As seen in Fig. 38, there is a considerable performance difference between the two sources for Case Two, where the U1 source requires 6.0 dB less power than the U2 source on order to achieve a BER of 10−5, while this distance has been reduced to about one dB for Case One.

VI. CONCLUSIONS AND FUTURE RESEARCH A. CONCLUSIONS We commenced by outlining the motivation of using DSC schemes in the real-world application of a hyperspectral image transmission scenario in Sec. I. Both the main principles as well as the historical background concerning both FIGURE 37. EXIT curves that characterise each user’s Phase-I the theory and practice of DSC were presented in Sec. II. transmission schemes of Fig. 25 with for ρ = 0.7 when communicating Furthermore, the paper’s outline and our novel contributions over an uncorrelated Rayleigh fading MAC, where the U2 sequence is punctured using Rp = 2/1. The simulation parameters are summarised were highlighted. in Table 8. Motivated by the example presented in Sec. I and by the excellent performance associated with the bandwidth- efficiencnt TTCM schemes, in Sec. IV we conceived a TTCM-aided DJSC design relying on perfect side- information, which resulted in our DJSTTCM scheme. A modified symbol-based MAP algorithm was proposed in Sec. IV-B relying on the idealised simplifying assumption of having perfect side-information at the receiver. The proposed system outperformed the benchmark scheme dispensing with joint decoding, almost regardless of the of cross-over probabilities. Explicitly, the benefits of having perfect side- information were demonstrated in Sec. IV-C. For example, for ρ = 0.90 and at a BER of 10−5 our DJSTTCM-16QAM scheme had a performance gain of 4.8 dB when compared to the non-joint benchmark, as seen in Fig. 19. The theoretical SW/S bounds, when communicating over uncorrelated Rayleigh fading channels were evaluated in Sec. IV-D where FIGURE 38. BER versus SNRt performance of the cooperative our proposed DJSTTCM-QPSK/BPSK scheme was shown DJSTTCM-SPM scheme of Fig. 25 for a correlation of ρ = 0.7, for Case = One and Case Two, when all systematic bits of U2 are punctured. The to operate within 2 dB from it, for ρ 0.93 at a BER simulation parameters are summarised in Table 8 and Table 10. of 10−5 as documented in Fig. 20. Our proposed scheme shows a beneficial compression capability, since it operates within 0.13 bits from the maximum achievable compression Hence, the near-error-free transmission of U2 cannot be guar- rate of the above-mentioned scenario, as seen in the rate- anteed for all identical transmit power and correlation. The region graph of Fig. 23. difference in the required transmit SNR can be readily seen In Sec. V, we have eliminated the idealised simplify- in Fig. 37, where U2 requires about 4.0 dB more power for ing assumption considered in Sec. IV. More explicitly, we creating an open EXIT tunnel leading to an infinitesimally have proposed the DJSTTCM scheme-aided SPM of Fig. 25 low BER. Although only the parity bits of the source U2 are for cooperative transmission arrangement of Fig. 24. Dur- transmitted, our powerful scheme was able to successfully ing Phase-I transmission, both source outputs’ were TTCM detect the systematic bits even for a relatively low correlation encoded and then compressed before transmission through a of ρ = 0.7 i.e. when the correlation related gain is lim- uncorrelated Rayleigh fading MAC, rather than assuming the ited. Thus, this difference was almost perfectly compensated, availability of an error-free side-information from one of the when applying an SPM scaling factor of r2 = 0.894 for the sources as in Sec. IV. Additionally, The EXIT chart of Fig. 28

1964 VOLUME 4, 2016 A. J. Aljohani et al.: DSC and Its Applications in Relaying-Based Transmission

TABLE 12. SNR threshold values of various schemes when transmitting over uncorrelated Rayleigh fading channels of Phase-I and Phase-II links, where ρ denotes the correlation coefficients, while r1 and r2 represent the SPM weighting factor pair. The results are extracted from Fig. 29 and Fig. 36.

was conceived to design the design the Phase-I transmission the source correlation for improving the attainable perfor- as follows: mance even when one of the user’s sequence is heavily punc- • The number of inner iterations I was determined from tured. It is worth noting that our the SNR threshold values in −5 the stair-case trajectories. at the target BER of 10 recorded for the various simulated schemes are summarised in Table 12. • The number of outer iterations Iout was determined from the outer and inner curves combination that facilitate an open EXIT channel. B. FUTURE RESEARCH In Sec. V-B.3, the SW/S bound of Phase-I was derived using 1) NON-COHERENT CODED MODULATION FOR the DCMC capacity and it was shown in Fig. 29 that our DISTRIBUTED JOINT SOURCE-CHANNEL CODING scheme performs within 1.0 dB of the SW/S limit for ρ = 0.4 In all the schemes considered, we have assumed that the at a BER level of 10−5, and only 0.17 bits away from the SW receiver has perfect knowledge of the channel information, minimum comparison rate. i.e. the receiver knows the Channel State Information (CSI). Recall from Fig. 24 that both users were assisted by a RN In realistic applications the receiver has to estimate the CSI that invokes the SPM scheme of Fig. 34, during Phase-II. either blindly or using training symbols [131]. For example, Different amounts of transmit power can be allocated, by in the Pilot Symbol Assisted Modulation (PSAM) scheme means of the SPM constellation ratios, for each user’s signal known pilot symbols are inserted into the transmitted data according to the integrity requirement. EXIT charts based streams for helping the receiver to estimate the CSI. This investigations were used for examining the decoding conver- comes at the expense of an unavoidable effective throughput gence and for optimizing the overall system. As demonstrated loss due to the associated pilot overhead. Alternatively, dif- in Fig. 36, performance gains of 2.8 dB and 3.4 dB were ferentially encoded transmission and non-coherent detection achieved at a BER level of 10−5 when ρ = 0.8 for SPM constitute attractive design alternatives that do not require the ratios of r1 = 0.894 and r2 = 0.447, respectively, comparing knowledge of the CSI [132]. More explicitly, non-coherent to similar schemes dispensing with our joint decoding. Fur- schemes should also be investigated. However, non-coherent thermore, it was demonstrated in Fig. 38 that our cooperative detectors generally exhibit a 3.0 dB performance loss in DJSTTCM-SPM scheme of Fig. 25 is capable of exploiting comparison to coherent detection having perfect channel

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FIGURE 39. Schematic diagram of mapper and demapper, where the transmitted signal is mapped using QPSK-based Set-Partition labelled mapping.

knowledge at the receiver [132]. Thus, we should also con- AWGN channel having a variance of N0/2 per dimension can sider the employment of non-coherent schemes, such as be written as: soft-decision-aided Differential Amplitude and Phase-Shift 2 ! 1 y − x(m) Keying (DAPSK) [133], [134] for low-complexity wireless Pr y | x = x(m) = exp − , (44) communications, since it dispenses with high-complexity πN0 N0 channel estimation. where m ∈ {0, 1, 2, 3}, as shown in the table of Fig. 39. Accordingly, the probability Pr x = x(m) | y can be further 2) HIDDEN MARKOV CORRELATION MODELLING expressed using Bayes’ theorem as [108]: The correlation between sources may be modelled using (m) (m) (m) a BSC, which is suitable for modelling the correlation of Pr x = x | y = Pr y | x = x Pr x = x memoryless sources. However, most practical sources exhibit N b memory [135], where similar to [136] a hidden Markov = | = (m) Y = (m) Pr y x x Pr bj bj . model can be used for modelling the source correlation. Thus, j=1 our next contribution will assume hidden Markov correlation (45) models by exploring the modiﬁcation needed in both the th DJSTTCM encoder and decoder. Given Equation (45), the probability that the i bit equals to B, where B ∈ {0, 1}, given that y was received can be APPENDIX A expressed as: X PROBABILITY CONVERSION Pr (b = B | y) = Pr x(m) | y , (46) This appendix details the conversion between LLR and prob- i (m)∈ ability, which is used in both Sec. IV and Sec. V. Consider x f(i,B) m the transmission schematic shown in Fig. 39, where the input where x( ) belongs to the subset f(i, B) which indicates that th (m) sequence {b1, b0} is mapped to the QPSK signal before its the i bit of x equals to B. More explicitly, Equation (46) transmission. Denoting the binary ‘‘one’’ as +1 and binary can be further expanded using: − ‘‘zero’’ as 1, the LLR for a bit bt may be expressed as:  all j  X (m) Y (m) Pr(b = +1) Pr (bi = B | y) = Pr y | x (Pr b . = t j L(bt ) ln , (41) (m)∈ j6=i Pr(bt = −1) x f(i,B) (47) where it is shown in [108] that the bit probability for bt can be estimated using: For example, given x(m) that is deﬁned using the table in Fig. 39, the probability of b1 = 0 can be written as: exp(−L(b )/2) Pr(b ) = t · exp (b L(b )/2) , (42) t t t Pr (b1 = 0 | y) 1 + exp(−L(bt ))  all j  = C · exp (bt L(bt )/2) . (43) = X | (m) Y (m) Pr y x Pr bj  exp(−L(b )/2) The term C = t is constant, since it is indepen- x(m)∈ (1, 0) j6=1 1+exp(−L(bt )) f (0) dent of the bt value. = Pr y | x = x Pr (b0 = 0) Returning to our example of Fig. 39, the channel proba- (1) bility of receiving y given x = x(m) was transmitted over an + Pr y | x = x Pr (b0 = 1) . (48)

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SOON XIN NG (S’99–M’03–SM’08) received LAJOS HANZO (F’04) received the D.Sc. degree the B.Eng. (Hons.) degree in electronics engi- in electronics in 1976, the Ph.D. degree in neering and the Ph.D. degree in wireless com- 1983, and the Doctor Honoris Causa degree munications from the University of Southampton, from the Technical University of Budapest, in Southampton, U.K., in 1999 and 2002, respec- 2009. During his 37-year career in telecom- tively. From 2003 to 2006, he was a Post-Doctoral munications, he has held various research Research Fellow working on collaborative and academic positions in Hungary, Germany, European research projects known as SCOUT, and the U.K. Since 1986, he has been with NEWCOM, and PHOENIX. Since 2006, he has the School of Electronics and Computer Sci- been a member of the Academic Staff with the ence, University of Southampton, U.K., as the School of Electronics and Computer Science, University of Southampton. Chair in Telecommunications. He has successfully supervised over He is involved in the OPTIMIX and CONCERTO European projects as well 80 Ph.D. students, co-authored 20 John Wiley/IEEE Press books in as the IU-ATC and UC4G projects. He is currently a Senior Lecturer with mobile radio communications totaling in excess of 10 000 pages, the University of Southampton. His research interests include adaptive coded authored over 1300 research entries at the IEEE Xplore, acted as the modulation, coded modulation, channel coding, space-time coding, joint TPC Chair and General Chair of the IEEE conferences, presented keynote source and channel coding, iterative detection, OFDM, MIMO, cooperative lectures, and received a number of distinctions. He is directing 100 strong communications, distributed coding, quantum error correction codes, and academic research teams, working on a range of research projects in the joint wireless and optical-fiber communications. He has authored over field of wireless multimedia communications sponsored by the indus- 150 papers and co-authored two John Wiley/IEEE Press books in this field. try, the Engineering and Physical Sciences Research Council, U.K., the He is a Chartered Engineer and a fellow of the Higher Education Academy European Research Council’s Advanced Fellow Grant, and the Royal in the U.K. Society’s Wolfson Research Merit Award. He is an enthusiastic supporter of industrial and academic liaison and offers a range of industrial courses. He is a fellow of the Royal Academy of Engineering, the Institution of Engineering and Technology, and the European Association for Signal Processing. He is also a Governor of the IEEE VTS. From 2008 to 2012, he was the Editor-in- Chief of the IEEE Press and a Chaired Professor with Tsinghua University, Beijing. His research is funded by the European Research Council’s Senior Research Fellow Grant. He has over 17 000 citations.

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