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On the Impact of Optimal Modulation and FEC Overhead on Future Preprint, 14/09/2021, 17:49 1 On the Impact of Optimal Modulation and FEC Overhead on Future Optical Networks Alex Alvarado, David J. Ives, Seb Savory and Polina Bayvel Abstract—The potential of optimum selection of modulation paradigm, any route reconfiguration can be accommodated and forward error correction (FEC) overhead (OH) in future through the network. However, this leads to over provisioning transparent nonlinear optical mesh networks is studied from an of resources. information theory perspective. Different network topologies are studied as well as both ideal soft-decision (SD) and hard-decision The increase in traffic demand together with the devel- (HD) FEC based on demap-and-decode (bit-wise) receivers. When opment of software-defined transceivers that can adapt the compared to the de-facto QPSK with 7% OH, our results show transmission parameters to the physical channel have increased large gains in network throughput. When compared to SD-FEC, the interest in designing networks that utilize the resources 12 HD-FEC is shown to cause network throughput losses of %, more efficiently. The degrees of freedom in the transceiver 15%, and 20% for a country, continental, and global network topology, respectively. Furthermore, it is shown that most of include, e.g., the forward error correction (FEC) scheme, FEC the theoretically possible gains can be achieved by using one overhead (OH), modulation format, frequency separation (in modulation format and only two OHs. This is in contrast to the flex-grid networks), launch power, and symbol rate (see [5, infinite number of OHs required in the ideal case. The obtained Fig. 3]). The network resources can be better utilized if these 5 80% optimal OHs are between % and , which highlights the degrees of freedom are jointly optimized in conjunction with potential advantage of using FEC with high OHs. the routing of the optical light path through the network. Index Terms—Bit-wise receivers, channel coding, forward er- To cope with increasing capacity demands, future optical ror correction, modulation, soft-decision, optical networks. networks will use multilevel modulations and FEC. This com- bination is known as coded modulation (CM) and its design I. INTRODUCTION AND MOTIVATION requires the joint optimization of the FEC and modulation The rapid rise in the use of the Internet has led to increasing format (see Fig. 1). The optimum receiver structure for CM traffic demands putting severe pressure on backbone networks. is the maximum likelihood (ML) receiver, which finds the The transport backbone of the Internet is formed of optical most likely coded sequence [6, Sec. 3.1]. The ML solution mesh networks, where optical fibre links connect nodes formed is in general impractical, and thus, very often the receiver is of reconfigurable optical add drop multiplexers (ROADMs). implemented as a (suboptimal) bit-wise (BW) receiver instead Studying the ultimate transmission limits of optical mesh [6, Sec. 3.2]. In a BW receiver, hard or soft information on networks as well as the optimal utilization of the installed the code bits is calculated first, and then, an FEC decoder is network resources is therefore key to avoid the so-called used (see the receiver side of Fig. 1). In other words, practical “capacity crunch” [1], [2]. receivers decouple the detection process: symbols are first Installed optical mesh networks utilize wavelength routing converted into bits, and then, FEC decoding is applied. In this to transparently connect source and destination transceivers. paper we consider BW receivers with both soft-decision FEC The quality of the optical communication signal degrades due (SD-FEC) and hard-decision FEC (HD-FEC). BW receivers to transmission impairments, which in turn limits the maxi- have been studied for optical communications in, e.g., [7], mum achievable data rate. This degradation is usually due to [8], [9] the amplifiers in the link as well as nonlinear distortion due to Traditional analyses of optical networks assume a target pre- neighboring WDM channels. Furthermore, the optical signals FEC bit error rate (BER), and thus, an HD-FEC with fixed OH arXiv:1508.04716v2 [cs.IT] 20 Aug 2015 within a transparent wavelength routed network travel a variety is implicitly assumed.1 Although the most common value for of distances, and thus, experience different levels of signal the OH is 7%, higher OHs have become increasingly popular. degradation. The most conservative design alternative for an Furthermore, the use of SD-FEC with high OHs (typically optical network is to choose the transceiver to operate error- around 20%) is considered the most promising FEC alternative free on the worst light path, i.e., for transmission between the for 100G and 400G transceivers. Although from a theoretical furthest spaced nodes [3, p. 138], [4, Sec. 1]. Under this design point of view, fixing the OH is an artificial constraint that reduces flexibility of the CM design and reduces the network Research supported by Engineering and Physical Sciences Research Council throughput, there are good reasons for fixing the OH. The (EPSRC) through the CDT in Photonic Systems Development and the project UNLOC (EP/J017582/1), and by the Royal Academy of Engineering/The client rates are usually quantized to 10, 40, 100, 400 Gb/s for Leverhulme Trust Senior Research Fellowship. This work was presented compatibility with the Ethernet standards. The symbol rate is in part at the 2015 Optical Fiber Communication Conference (OFC), Los also often fixed to accommodate the transmitted bandwidth Angeles, CA, Mar. 2015. The authors are with the Optical Networks Group, Department of Electronic and Electrical Engineering, University College London, London WC1E 7JE, 1When SD-FEC is considered, however, pre-FEC BER does not determine United Kingdom (email: [email protected]). the FEC OH, as recently shown in [10]. 2 Preprint, 14/09/2021, 17:49 1 − Hb(BER) m Pk=1 I(Bk; Lk) HD BW Receiver I(X; Y ) Hard-Decision Bˆ Iˆ CM Transmitter MQAM HD-FEC Demapper Decoder I FEC Encoder B X Y MQAM Mapperm Optical Channel Rate Rc with M = 2 SD BW Receiver Soft-Decision L Iˆ MQAM SD-FEC Demapper Decoder Fig. 1. Coded modulation system under consideration. At the transmitter, a binary FEC code is concatenated with a M-ary QAM modulator. After transmission, the noisy received symbols are demapped and then decoded by a bit-wise receiver. When the demapper makes hard decisions on the symbols, an HD-FEC is used. When the demapper computes log-likelihood ratios (soft-decisions), an SD-FEC is assumed. The achievable rates discussed in Sec. III are also shown. into a given fixed-grid, leading to fixed OHs. Under these In this paper, we study the problem of finding the optimal constraints, no full flexibility on the selection of OHs is pos- modulation and FEC OH from an information theory view- sible. In this paper, however, we will ignore these constraints point. In particular, we use information theoretic quantities and focus on finding the theoretically maximum network (i.e., achievable rates) and a realistic model for the nonlinear throughput. interference to study the maximum network throughput of To increase the network throughput, different approaches optical mesh networks. For point-to-point links, and under a have been investigated in the literature. For example, [11] Gaussian assumption on the channel, the solution depends only considered mixed line rates (10, 40, 100 Gb/s) for the NSF on the signal-to-noise ratio (SNR). For an optical network, mesh topology, [12] considered variable FEC OHs with fixed however, the solution depends on the SNR distribution of symbol rate and modulation formats, and [13] considered the connections. Therefore, the theoretically optimum CM variable modulation format and SD-FEC OHs. Adaptive FEC design is obtained when the modulation size and FEC OH based on practical codes was recently considered in [4]. are jointly designed across the network. Significant increases Variable OHs with 16QAM and 64QAM were studied in [14], in network throughput are shown. Furthermore, practically where probabilistically-shaped constellations were considered. relevant schemes (based on either one or two OHs) are also The optimal modulation format based on an approximation considered, and their gap to the theoretical maximum is quan- for the maximum achievable rates of HD-FEC was consid- tified. This paper extends our results in [39] by considering ered in [15]. Adaptive FEC OH for time frequency packing multiple network topologies as well as both HD- and SD-FEC. transmission was studied in [16] and [17]. The problem of This paper is organized as follows. In Sec. II the system routing and spectrum assignment for flex-grid optical networks model, network topologies, and physical layer model are with orthogonal frequency-division multiplexing was studied described. In Sec. III the optimal selection of modulation and in [18]. The key enabling technology for these approaches are coding is reviewed and the maximum network throughput is software-defined transceivers, allowing for example to vary the analyzed. In Sec. IV practically relevant schemes are consid- modulation format and symbol rate, as done in [19], [20], [21], ered. Conclusions are drawn in Sec. V. [22], [23]. In [24], [17], a software defined transceiver with variable FEC was experimentally demonstrated. II. PRELIMINARIES To optimize the network design, a physical layer model is required. While in the past very simple models (e.g., reach- A. System Model based models) were considered, recently, nonlinear effects We consider the CM transmitter shown in Fig. 1, where a bi- have been taken into account using the Gaussian noise (GN) nary FEC code maps the information bits I = [I1, I2,...,Ikc ] model [25], [26], [27], [28], [29], [30], [31]. In [32], the into a sequence of code bits B = [B1,B2,...,Bnc ], where closed form solution of the GN model of [31] was used to Rc = kc/nc is the code rate.
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