Coding Techniques in High Speed Telephone , a survey

M.Maspaitella

Eindhoven University of Technology

Faculty of Electrical Engineering Group Information and Communication Theory

march, 1991

Coaches: ir. P.G.M. de Bot (TUE), ir. F. van Terwisga (PTH) Abstract

In this literature study report, several aspects of coding techniques will be described. ASK, PSK and QAM as major M-ary constellations will be discussed theoretically in order to get an insight of the fundamental principles of digital communications over a band-limited channel. An important factor is the relation between signal energy Es and the minimum Euclidean distance between adjacent points in a constellation. Subsequently, coding schemes with block coding and, more profound, convolutional coding are discussed. Next topic is the trellis coded achieving coding gain with a redundant hit. Based on the theoretical introductions in the proceeding chapters, relevant CCIlT recommendations for modems up to 14.4 kbps will be discussed. From several scientific and commercial sources, information was obtained about the most recent technical developments in high speed modems. Data rates up to 24 kbps are achieved by application ofhighly advanced coding principles. Multicarrier modulation, multidimensional signal constellation, multilevel coding, and trellis precoding are state of the art design principles discussed only in a introductory way. Finally a number of 'mile stones' are surveyable adapted in a table. Preface

November 1990 a study was initiated to investigate the performances of present high speed modems. The (literature) study should support a current research project at the group information and communication theory at the faculty of electrical engineering of the TUEl. The literature study was carried out as an alternative study project in 2 the last year on the Pedagogisch Technische Hogeschoo1 • After deliberation hetween the author and the concerning institutions, it was agreed to perform a literature study during approximately 6 weeks.

Coaches during this project were Paul de Bot from the TUE and Friso van Terwisga as a supporting teacher from the PTH. Practically, research and editing activities were carried out at the TUE Faculty of Electrical Engineering, group Information and Communication Theory.

Main purpose of the study was to obtain recent technical information about recent high speed telephone modems. A survey of recent modem designs was required. From different sources several kinds of information were obtained. Specific interest was fixed on coding techniques and performance as well. To support the literature study sufficiently, it was necessary to provide a theoretical description ofdigital coding techniques. As an important spin-off, a summary of existing coding techniques had to be written. This part of the report seemed quite useful as a first introduction in coding techniques. However, for a more in depth study, the reader is referred to other excellent books ahout digital communications.

An optional extent ofthe project wac; to demonstrate an (electrical) ac;pect of a telephone modem. However, the remaining time did not allow to complete this part of the project. A brief study learned that applying modems in an experimental set-up requires a large amount of complex equipment and more research determine practical goals.

lEindhoven University of Technology, P.O.B. 513, 5600 MB Eindhoven, The Netherlands.

2The Pedagogisch Technische Hogeschool in Eindhoven is a higher technical educational institute, for teachers in technical disciplines. The author is a student at the elektrotechnical department of the PTH. PTH Eindhoven, P.O.B. 826, 5600 AV Eindhoven, The Netherlands. TABLE OF CONTENTS

1 Introduction 6 1.1 Working approach 6 1.2 Content of the report , 6

2 Useful definitions 7

3 Representation of modulated signals 9 3.1ASK 9 3.2 PSK ...... 10 3.3 QAM ...... 13

4 Noise 14

5 Minimal distance related to signal energy 16 5.1 4-ASK 16 5.2 4-QAM = 4-PSK 17 5.3 8-PSK 17 5.4 16 QAM 19

6 Multipoint Constellations 19 6.1 Other Constellations...... 21

7 Channel coding ...... 22 7.1 The communication system...... 22 7.2 Block coding 23 7.3 Convolutional encoding 24 7.3.1 Example of a convolutional encoder 24 7.3.2 The TrelIis Diagram 26

8 Trellis-Coded Modulation 27 8.1 The basic idea behind trelIis coding 28 8.2 The Viterbi algorithm ...... 28

9 Echo Cancelation 29

10 Coding techniques in operational telephone modems 30 Table 40

11 Recent technical developments 41 11.1 Multicarrier Modulation 41 11.1.1 Applications 41 11.2 Multilevel coding 42 11.2.1 Applications 42 11.3 Advances in trellis-coded modulation 42 11.3.1 Multidimensional trellis coding 43 11.3.2 Applications 43

4 11.4 Shaping 43 11.5 Adaptive bandwidth 44 11.5.1 Trellis precoding 44

12 Current high speed modems 45 12.1 Summary 45 12.2 Notes ...... 46 Table 47

References ...... 48

A Glossary Of Notations 50

5 1 Introduction

1.1 Working approach

In an early stage, documentation was requested from different suppliers. A study had to be made of coding techniques to get a sufficient understanding of the basic coding techniques. This was necessary to translate the scientific literature into an adaptable and readable introduction in PSK, ASK, QAM and trellis coding.

The study of relevant literature, and the writing of this report were the main part of this investigation.

1.2 Content of the report

Like the investigation, the report can be divided into two main parts.

The first part deals with a theoretical explanation of coding techniques, applied in modems. A brief summary of common telephone circuit techniques is provided as well. In the second part a survey will be presented of the high speed telephone modem market. At first some CCIlT standards and recommendations will be explained. Next, a summary will be given from recent developments on the high speed modem market. For this is a literature study, there are many references to relevant scientific and commercial articles. Features and performances of different models will be com­ pared. For reasons stated before in the preface, no further attention is paid to the attempt to visualize some effects with measuring equipment.

6 2 Useful definitions

To get some more insight in the working principles of modems, several basic aspects will be described in this chapter. First we will discuss some essential definitions

Transmission line

The telephone line as a data transmission line includes some typical properties. The Public Telephone Network, which is the backbone of most data communications, was originally developed for voice and not for data transmission. It is optimized for a satisfactory voice communication between telephone subscribers. As most voice energy is concentrated between 300 Hz and 2500 Hz, the bandwidth of a telephone circuit is approximately between 300 Hz and 3200 Hz in order to satisfy the average telephone voice subscriber. Therefore it is also called a band-limited channel. To protect other cables from being disturbed, The telephone company also limits the signal level to protect other cables from being disturbed wit Inter Symbol Inter­ ference (lSI).

Modem

A modem transmits binary data over a telephone line. This is achieved by modulating data bits onto a band-limited carrier signal. At the other end of the line the signal must be demodulated in order to obtain the digital data.

Keying

Digital information is characterized by the property that it always is represented in a discrete value. (e.g. +5V (one), -5V (zero» When we modu late an analogue carrier with discrete values, the signal is said to be coded or keyed.

Modem specifications

Baudrate

The baudrate expresses the number of different signal points the modem transmits per second. Hence this is also defined as the , as every point can be considered of a symbol-word defined by a bit, dibit, tribit etc.

Data rate

An important criterion to review a modem is to measure its data rate. The data rate indicates the speed of the incoming information bits that will be transmitted. The data rate is notated in bits per second (bps). At this moment high-speed modems offer performances up to a 19200 bps.

7 SiN ratio

The signal to noise ratio provides information of the signal level related to a given noise component on the transmission channel. This information is useful to have an impression of how 'loud ' the signal level must be, in order to make a distinction between noise on the channel and a transmitted signal. SiN is notated in dB.

Bit E"or Rate

The Bit Error Rate (BER) indicates the probability an error occurs. Usually, the performance of modems is expressed as a required SiN at a certain BER. For example, a BER of 10-6 can be achieved at a SiN of 30 Db.

Telephone line

To send (digital) information over a telephone line data must be modulated on an analogue carrier signal. A suitable carrier wave form is a sine wave. For digital applications we want the analogue signal to have a limited amount of discrete values. These: different values, or positions, can be achieved by several forms of modulation or coding. We can make a distinction between FSK, ASK, PSK and QAM. The data is protected for being disturbed (by ego noise) by coding techniques.

In the next paragraph the different modulation techniques will be discussed briefly. For a more in depth study of typical telephone techniques the reader is referred to [Bingham].

8 3 Representation of modulated signals

Representations from a modulated waveform, known from analogue modulation are:

Sj(t)-Aj(t)cos(wt+4>,) A j: Amplitude 4>,: Phase

Otherwise:

Sj(t)-Aj(t)cos(wt+4»­ x(t) coswt+y(t) sinwt

quadrature components x(t)-Aj(t)cos4>, and y(t)-A j(t)sin4>,

unit vectors coswt and sinwt

x(t) and y(t) can be considered as two low-pass signals, modulated on two orthogonal unit vectors in a two dimensional signal space. The angle between the unit vectors is 90·.

Unit vectors not only have a direction but a certain length as well. The rea~on for translating functions into a vector space deals with the fact that from now on all kinds of modulation can be modelled in a surveyable vector diagram.

3.1 ASK

First it's obvious to change the amplitude of the sine wave. Suppose we want the sine carrier to have two discrete values. The change in amplitude is accomplished by a binary '1' and binary '0'. If we want to change the signals' amplitude, it is possible to 'switch' the carrier on and off by a binary 1 or O. This technique is called Amplitude Shift Keying (ASK).

For ASK the general expression is

O~t~T sj-Aj(t)cos(wt) . ) ( 1-1,....M

The amplitude term A; will have M discrete values, and the phase term phi is constant.

9 Figure 1 Amplitude Shift Keying (On Off Keying)

Of course the signal can express more then two values. If we give the signal 4 possible amplitude values to express, every single level or value represents a certain 2-bit comhination. (note that 2 hits result in 4 possihle combinations) Hence the 2-bit comhination is also cal1ed a dibit. It should he noted that the different signal points normal1y will he assigned to a Gray-code. Adjacent points only differ 1 bit.

•_------<,...... -. i,l t) --0-'-- .>--~------+-._.i,l I) ,os, S, S, 0 Sj s. 1/ = 2 M= 4

2M . . .. . • 1,(1) ., s, Sj 0 s. S, s. M=6

Figure 2 ASK constellations

In general, ASK can be expressed as a one dimensional transition. Hence this can be represented in an orthogonal diagram in which ASK 'points' several discrete values. The different point are all located on one horizontal axle. This implicates the one dimensional character of ASK.

3.2 PSK

Basical1y all different forms of Phase Shift Keying are hased upon the principle of 2-phase shift keying (2-PSK). In PSK the phase angle of the carrier is directly altered hy the value of the digital signal.

M = 2 ~..----~."',(t) 12 s,

Figure 3 2-PSK

10 For binary transmission we would have

Obit; 0 0 1 bit; 180 0

The general analytic expression for PSK is

~ St(t)- -cos(<.t.>t+-)2E, 2lti i-O.l...M-l TMs

Es is the signal energy per symbol

is an expression for the signal amplitude because

T,

f [sj(t)fdt-Es sj(t)-Acos(<.t.>t+4» o

T, -A2f%(1 +cos(2<.t.>+4»)dt o A 2 1. ) T;s --[t+-sm(2<.t.>t+4> ]0 2 2<.t.> 2 _ A (T +_1-sin(2<.t.>T +4»-_l-sin4» 2 s 2<.t.> s 2<.t.> -Es fOT all 4> >- sin(2<.t.>T +4»-sin4>>-2<.t.>T -2hr>-T _ Ttk s s s <.t.> 2 >- __A Ts_E 2 s

11 Note that a O· and 180· phase change results in a one dimensional reversion, which implicates an inverted signal. Hence, 2-PSK = (2-ASK).

Two-bit codes called dibits can be transmitted in this manner, using 4-PSK 4-PSK involves 4 different phase-positions. Hence this corresponds with phase shifts at 90·, 180· and 270·. The four phase-positions can be transmitted on two orthogonal components of the carrier signal. 4-PSK = (2_ASKf-dimensional Therefore 4-PSK is also called 4-Quadrature (4-QAM). 4-PSK is shown in the other figure

8-PSK is comparahle to 4-PSK, but now with twice as much points in the orthogonal space. Each point represents a "trihit" (eg. 000, 001). Note that the space hetween the points has decreased with almost half the distance.

Considering the 4-PSK and 8-PSK constellation, the radius is having the same length. Note, this implicates that the amplitude, or envelope, of the signal has not increased.

Hence this means that E 5 remained the same.

As a drawback however, the possihility that two points, lying closely to each other, can be confused has increased. Generally, in most cases tribits are mapped on the signal points using a Gray-code. PSK is a preferred process when transmission at high rates is desired. One important reason is that is applied directly to the carrier and does not require modulation of the carrier frequency. In band-limited channels a stable carrier frequency is required.

011 01 OI'/~JAool , A / \ II 00 II ~:~ / !oo000 I~O 10

M" 4.). '" 0 M:: 8.). = 0

(al ,e)

011 001 I~ 010/ A ~\OO(J ! /\

III 101 ""u'·M::8,)''''./8 'hi 'dl

Figure 4 PSK for M =8

12 3.3 QAM

Data transmission at 9600 hps over a voice channel can he accomplished hy packing four bits at 2400 haud using a technique known as quadrature amplitude modulation (QAM). This method can he descrihed as a comhination of phase modulation and amplitude modulation. For example; 8 values of phase and three values of amplitude can produce 16 possihle signals (16­ QAM).

~--- ...... ---... ----.- - ...... ----.---...-----.,...·64 I I I i I ... = 32 , + /r- ----+------.- ---...... , I : /// '" I I / M .. 16 " I t ' r----... - --+----., 1 r I :: :I: III I: I ~ t '----T- -....,-:~:q •• ---r------r-iIIII-:-r---:-i-:--t--1.41=4 III -- • • t-----+--+-....i..--- •• : : I I 1TIII

tI',t, L--"-I'-- ...1---2/t--1---lT / J 1i l', ///: • ~---,,--,-_-----4 • I 1 I i I : ~--- ...... ---.... --- ... -J--.... ----.----+--- j

d~" - 2.(, Figure 5 Rectangular QAM signal constellations.

The signal constellation for M-ary QAM consists of a 2-dimensional square lattice of message points, as illustrated in the figure above. The corresponding signal constellations for the in-phase and quadrature components of the amplitude phase modulated wave are shown in figure 5. The hasic format of the constellation can he recognized as a combination of two L­ ary ASK constellations. In two dimensions the QAM constellation enahles the transmission of M = L2 independent symhols.

The mathematical expression for M-ary QAM is identical with the general equation for orthogonal signals, where both amplitude and phase are a function of time;

13 aj and bi are a pair of independent integers chosen in accordance with the location of the pertinens message point. This expression can be expanded in terms of a pair of basis functions:

~I(I) - ~cos(<.>1) O

~,(t) - ~ ~sine <.>1) 0

4 Noise

In this chapter we will discuss briefly some relevant aspects of the noise phenome­ non. The term noise refers to unwanted electrical signals that are always present in electrical systems. The presence of noise superimposed on a signal, tends to obscure or mask the signal; it limits the receiver's ability to make correct symbol decisions, and thereby limits the rate of information transmission.

Among several kinds and sources of noise there is one natural source of noise, called thermal or Johnson noise that cannot be eliminated. The thermal noise can be described as a zero-mean Gaussian random process. The effect on the detection process of a channel with additive white Gaussian noise (AWGN) is that the noise affects each transmitted dimension independently.

...... :~:: ... . '. :.~.:-:.

Figure 6 Perturbation of transmitted signal points.

14 In a two-dimensional vector space a 4-PSK constellation can be illustrated by 4 different vector points. As an effect of noise, transmitted points will be perturbed by noise so that the actual received vector will be a resultant of a signal vector and a noise vector. To ensure that a received vector will not be confused, the noise vector must be limited to a certain maximum. This means that the chosen points in a constellation must be separated by a minimum distance.

Example of binary detection in gaussian noise Decision line Region 2 . Region 1

Likelihood of 52 Likelihood of 5, p(z I 52) p(z I 51)

~~...... ::::====~ z(T)

Figure 7 Noise probability functions

Figure 7 illustrates the probability density of the output Z(t) for Sl' or S2 was transmitted, also called the likelihood of SI and the likelihood of S2' The threshold level must be chosen optimally for minimizing the probahility of making an incorrect decision. In this case the decision level must be located in the centre between al and a2• If P[all = P[a2l

15 5 Minimal distance related to signal energy

A comparison of different coding techniques

In this chapter a number of different constellations will be considered to demonstrate the relation between signal energy E s' vector points and minimal distance dmin • The minimum Euclidean distance is an important factor because it determines the sense to noise. Constellation points with a small distance in between can relatively ealiY be disturbed. As mentioned before, a telephone channel has typical limitations for both bandwidth and signal level. Consequently the amount of transmission power is limited. It will seem that different constellations offer different minimum distances related to signal energy.

E s divided by the number of information-bits calculates the bit energy Eb•

5.14-ASK

A 4-ASK constellation can simply be obtained by coding a dibit. The signal's carrier amplitude can vary in four discrete values. As shown in the next figure,

Figure 8 Distances in a 4-ASK constellation

four points are located on the horizontal axis, with relative distance dmin • Es can be calculated by taking the average Euclidean distance from the different signal points to the origin. The Euclidean distance is determined by the length of the signal vector. Generally, we calculate the squared distance in a constellation by:

f2E; A - ~ -t (see section 3.2)

In this example, the signal energy totals twice the bit energy. A signal point is produced by two bits.

16 5.2 4-QAM = 4-PSK

2 dDUll. -2Es-4Eb

General the performance of different constellations can be compared by determine the asymptotic gain. The 4-ASK can be compared with the 4-PSK constellation by determine the a~ymptotic gain

2 G- dmin,B -~-2.5-3.6dB - 2 1.6 dmin.A.

The asymptotic gain is always determined by the bit-energy values. Note, we only compare schemes with equal spectral efficiency,

'lA-T'lB '1: - number of information bits I 2-dimensional signal

5.38-PSK

M-Phase Shift Keying (M =8, 3 bits/symbol)

d~-(2-Ii)Es

-3(2-Ii)Eb

-1,76Eb

17 ., -,fC

\ \ \ \ \ \ \ \ \ \ -_ \ I _ -_ \ I _- -...:,fC:....:E+ -~-~- \+/.:::~:-~_~ +,fC-£ •• _.... --I \--\ -_ .... - I \ - I\ I\ I\

I I " \ I \ I \ I \

-,fC

Figure 1 8-PSK constellation.

18 5.416 QAM

2 (M=16, m=4)Jn this case dmin is equal to the minimal distance compared with 4­ ASK, which can easily be seen from the next

·64 ~---.....----...----.- - .....----.---....------..,... I I I : I .... n • ~----+-- --.----.. • • + / "I I / 1 ',I l /// 1 M :: 16 " \ t f r----o--t------, ., · I I' ::: III III III M _ 8 j II • + ---.,..---~ IIII+----....-- 1'1'4 III•• I +- -+-_ .~ .L_ ::I::I: i , • ....---.-.-- --4.----1 •• I ': I.1 :: I I I i ll~(' I I III '1 II • ~ .... ---..- --0----" ) • 1 "" f--2r"--l / I I', /// l t" / I • --..----..- --+----.... • I I I I I I tL---- ...... _ --..----.... ----+------l

Figure 10

6 Multipoint Constellations

Several multipoint constellations have been developed to reach an optimum for specified conditions. But each of the constellations has some of the following disadvantages: they are difficult to generate and even more difficult to detect optimally in the receiver. General: multi-point constellations with M signal points are called M-ary constel­ lations. Subsequently, m = 21 0g M

Consequently, if m is even, then square constellations, in which M/2 bits are used independently for each dimension, are now most often used.

If is m odd a simple square in not possible. Generally the shape of the constellation will be a cross.

For m =3 three alternatives have been used; an eight phase configuration and two 'stars'. The star in figure b is theoretically preferahle because it's total power is less for the same dmin between points. However, the signal constellation is difficult to generate by analog techniques. Therefore the star in Fig. c was chosen for the 4800 hitls fall­ back mode of V.29.

19 For M = 5 and 7 the almost crosses were proposed and codified by U ngerboeck.

·t· ::~ -;r- ...... ••2 ...... ::r: ...... +n.' ...... a 2. 3a ...... +r'0' ...... ITf-n.' ta=2t'>.",!or Campopiano/Glazer COIl8lellallons. n odd). Fill. 4. Cr0S3 COIISt<:lIation boundary. ·...... ··...... ·.....·... .. ·...·...... ·... . .

n-8 CI'08ll (S_41)

no' Fill. 3. RCCIaD8ular sipaI COIISt<:llauons (alter CampopiaDo aDd Glaur (91l

n_8 cln:uIar (S-4O.8) Fill. S. Imp""""" 'CCIaD8ular CODStdiations.

Figure 11 Examples of multipoint constellations.

20 6.1 Other Constellations

In a two-dimensional space, the densest lattice is the hexagonal lattice. Therefore constellations using points from a hexagonal lattice ought to be most efficient. A typical feature of hexagonal constellations is shape ofthe decision-regions around the single points. A drawback from hexagonal constellations however is that detection is more difficult comparing to square decision regions.

6J6 IIII!E IOUUlAI. ON 1EUCnD ...... 1N COIDftJNICAnONS, VOL ""c-2. NO. S,"""""'" 1984 ...... n-2 S_2(3.OdB) n.3 + n_4 S_4.3125+(6.3dB) S. 6.75 (9,4

......

...... n-S ...... Sa 17.59 (12.SdB) ...... ••3 5_4.5+(6.5c:lB)

n_6 ••1 8_35.25 (IS.5dB) a••.C375 (15.5ce) Fi&. 6, Optimum beuaoaal OOIU1

Figure 12 Hexagonal constellations.

Figure 12 is showing the best hexagonal packings for m =2 through 6. The m=3 constellation was used in a 4800 bit/s Hycom modem. The rather strange-looking m =4 constellation is still the best 16 point constellation known. The m=6 structure is used in the Codex/ESE SP14.4 modem.

21 From other sources ,------, Information I Source Channel I source i bits bits : t I t t~~ Freq­ Mod­ uency Format ulate spread

Digital input C m, h a n n Digital e output I

Demod­ Format ulate .. I I t t ! Source Channel Information ~i~ sink iL bits _ _ J

_ Optional To other Essential o destinations

Figure 13 Block diagram of a typical communication system

7 Channel coding

7.1 The communication system

The block diagram of a typical communication system shows the basic elements. So far, the modulating techniques have been discussed briefly. Another important functional processing step is the encoding and decoding of the signal. Channel coding refers to signal transformations designed to improve communication performance by enabling the transmitted signals to better withstand the effect of various channel impairments, such as noise, fading and jamming. Usually, the goal of channel coding is to reduce the probability of bit error (Po), or to reduce the required En/No.

Channel coding ha~ become a popular way to provide performance improvement for band-limited channels in telephone modems. The use of large-scale integrated (LSI) circuits has made it possible to make a substantial performance improvement.

In general there are two ways to encode a bit stream signal; block coding and convolutional coding. Both will be described in the following sections.

22 7.2 Block coding

In calie of block codes, the source data are segmented into blocks of k data bits, also called information bits or message bits. Each block can represent anyone of 21,; dis­ tinct messages. The encoder transforms each k-bit data block into a larger block of n bits, called code bits or channel symbols.

The (n-k)bits, which the encoder adds to each data bJock, are called redundant bits, parity bits or check bits. Generally block codes can be expressed as folJows; the code is referred to as an (n,k)code with redundancy (n-k)jk and code rate n.

General expression block codes

[n,k,a] n;code word length k;number of information bits () ;minimum Hamming Distance

Examples for 8-PSK

[8,1,8]: repetition code.OOOOOOOO 11111111

[8,7,2] single parity check code: 7 bits + 1 parity bit

[8,4,4] extended Hamming code minimum Hamming distance 6 = 4 oooooooo 11111111 11110000 11001100 10101010 00001111 00110011 01010101 00111100 11000011 01011010 10100101 01100110 10011001 01101001 10010110

A more profound study of block codes can be found in [Proakis].

23 7.3 Convolutional encoding

The block encoder continuously segments the incoming data bits into blocks. The convolutional encoder is reading in single bits after each other into a shift register. An important characteristic of the convolutional encoder, different from block encoders, is that the convolutional encoder has memory. The incoming words are called k-tuples, the outcoming word of an encoder is also called an n-tuple.

General: constraint length K = # elements in the shift register. or, constraint length v = K -1 = # memory blocks

The n-tuple emitted by the convolutional encoding procedure is not only a function of an input k-tuple, but is also a function of the previous K - 1 input k-tuples. In practice, nand k are small integers and K is varied to control the redundancy.

The size of the n-tuple is greater than the k-tuple. The n-tuple contains an additional redundant bit.

Note that the velocity of outcoming n-tuples is equal to the velocity of incoming k­ tuples.

7.3.1 Example of a convolutional encoder

u \ First 1 I code symbol

Input bit ~_ • Output m r>-----.,~~branch word u \ Second 2 'I code symbol

Figure 14 Convolutional encoder (rate 1/2, K=3)

A convolutional encoder can be represented as a shift register with additional binary logic. In this example shown above, there is one input sequence of bits.

The register shifts the serial bits internally. The different register states are connected with logical functions (eg. OR's). The logical outputs produce two outcoming bit streams with different codes.

The n-tuple output from the convolutional encoder can be considered as two

24 m = 101-1 Encoder ~ u orthogonal components. The ratio n/k Time Encoder Output = 2/1 = 2. The constraint length K = 3. u, u, U2 t, ~ SO with every incoming bit, the en- U2 coder produces an outgoing n-tuple. The figure of the n-tuple is a function of k and K. As a consequence, the number of states of the n-tuple is limited to a fixed number of possible u, states. t2 ~ 0 U2 The n-tuples are directly related to the input k-tuples. The four possihle states of the n-tuple of the example are directly related to u, four unique input 'branches'. Note t3 ~ 0 0 that the shift register mechanism in U2 fact implicates a memory-function. The n-tuples have relation to the history of the k-tuples as well.

u, t4 ~ 0 U2

Output sequence: 11 10 00 10 11

Figure 15 Convolutionally encoding of a message with a rate V2 K=3 encoder

25 The function of a Convolutional encoder can also be visualized in a sequential state diagram,

00

Output /' branch word 11,#...... 11 ~ / / / 00

Encoder state

\ 10 " 01""- ...... Legend -- Input bit 0

---Input bit 1

Figure 16 Sequential state diagram of a convolutional coder.

7.3.2 The Trellis Diagram

Another more convenient way to represent the convolutional encoding process is the trellis diagram. From the previous example, it will be clear that the outgoing n-tuples, can only change in a limited sequence. Hence, it is possible to display this process in a graphical way.

t, 00 t2 00 t3 00 t4 00 State 8= 00 "- "- "- "- "- 11 "- ,,-11 "-"- 11 "- "- "- "- "- "- "- "- b= 10. "- "- \ \ \ \ \ c = 01 • \ • \ \ \ 01 \ 01 \ \ \ \ d = 11 • -----..... • 10 10 10 Legend Input bit 0 ----- Input bit 1

Figure 17 Encoder trellis diagram (rate ~ K=3)

26 In the trellis diagram, vertically are given the four binary states or n-tuples; 00, 10, 01, 11. Dependent on the configuration of the encoder, there are only a few state­ transitions possihle. The possible transitions are displayed with lines between the states.

The dashed lines refer to an input 1, and the solid lines refer to an input O. Note that the trellis diagram repeats with the same structure after the third branch. The trellis diagram shows an important property of the convolutional encoder; only certain transition 'patterns' are possible. This depends of both the incoming bit(s) at moment t and the encoder state at t-1. This illustrates the memory function of a convolutional encoder.

8 Trellis-Coded Modulation

Telephone modems operate within hand-limited channels. Increasing the data-rate generally results in an increase of the numher of signal points. Within a hand-limited channel, as a consequence, the numher of signal points will increase without an increase of the signal space. As an example, consider three different constellations, 4-ASK, 4-PSK, 16-0AM. (figure 18)

Hence, dmin between the points has decreased, so the probability of an error has increased.

Uncoded 4 -ary PAM UncOded 4 ·ary PSK Uncoded 'S-,Jry QAM

/ ..I' . I I

\ ~ ,, ..I· .

Rate 2/3 coded B·ary PAM Rate 2/3 coded B-ary PSK Rate 4/5 coded 32 ary QA\

I "\ • ,. ••••

, ---" I *...... " / ...... ~, _...... 101 -*(bl lei Figure 18 Increase of signal set size for trellis modulation

Convolutional encoding adds an extra bit to the outgoing n-tuple, so the numher of signal points increases.(eg. the rate 1/2 encoder doubles the k-tuple to a 2 hit n­ tuple, with four signal points) Because bandwidth expansion is simply not possihle for telephone channels, at first it seems that a convolutional code won't he useful hecause of the limited handwidth­ error prohahility.

However, trellis-coded modulation does achieve coding gain without bandwidth

27 expansion. At first this may seem contradictory with the principle described above. Trellis coding achieves coding gain at the expense of decoder complexity.

8.1 The basic idea behind trelJis coding.

The error performance of uncoded modulation (such as PSK, QAM) depends on the distance between the closest pair of signal points; dmin • The objective of trellis coding is to increase the minimum distance between the signal sequences that are most likely to be confused, without increasing the average power.

A convolutional encoder introduces a redundant bit, so the size of signal alphabet k k 1 n increases from 2 to 2 + =2 • This results in twice as many coded symbols as uncoded ones.

For example, a 4-PSK constellation expands with the addition of one redundant bit to 8-PSK. The expanded signal set does not result in an increased required bandwidth. The distance between adjacent signal points has decreased. The average signal energy did not change. However, the minimum distance between single possible code signal sequences determines the error performance. (remember that the convolutional encoder allowed only few transition codes) As a consequence the distance between allowable code symbol sequences has increased. This distance is also called the minimum free Euclidean distance. Therefore assigning signal points to the coded bits in a way that maximizes Euclidean distance is the key to optimizing the trellis codes.

Ungerboeck developed [Proakis] an assignment procedure, called set partitioning. More information about trellis coded modulation can be found in [Proakis].

8.2 The Viterbi algorithm

As stated in the previous sections, a convolutional encoding scheme 'permits' only few transitions. The trellis diagram represents the several transitions with lines between (encoder)states.

The trellis encoding scheme offers a possibility to detect and correct errors. Since the transition to a state is possible from different other states, the decoder has to determine which transition was most likely. The Viterbi algorithm [Proakis] is an decision mechanism to detect the most likely signal. Therefore the Viterbi decoder is known as Maximum Likelihood (ML) decoder for convolutional codes.

28 9 Echo Cancelation

A specific technique, described in V.32 is the echo canceller. Older modem techniques achieved full duplex operation by splitting up the signals in two different frequencies. In this way it was possible to make a distinction between received and echoed signals. With QAM coding however, both modems operate at a frequency of 1,800 Hz. As a result, a large number of extra harmonic frequencies is generated. Splitting up the frequencies is now not possible. [Humphrey]

Figure 19

Echo cancellation makes extensive use of high speed digital signal processors. Both sending and receiving modems transmit simultaneously at identical carrier frequencies, and the inbound and outbound data clash and overlap, interfering with one other. The modem knows what signals it just transmitted, transmitted 100 milliseconds ago, transmitted 2 seconds ago, and so on. It creates scaled and inverted copies of the waveforms that it transmitted and adds these onto the received data stream to cancel the interference from its transmitter, leaving only the incoming signal for its receiver to process. This is an incredibly complicated task that typically requires the service of DSPs with performance in the range of 25 to 50 million instructions per second. The automatic echo canceller is an active circuit that tunes the impedance to achieve distinction between sent and received signals.

29 10 Coding techniques in operational telephone modems

Modems can be defined as the translators between digital terminal equipment and analog transmission circuits. Voiceband modems may be separate units or built in to equipments. They may be one-way or full duplex, for private or dialled lines, and operate at data rates from 300 bits/sec to as high, at the time of writing, as 19,200 bits/sec.

10.1 Standardization

The CCITI, a world standards-making organisation has issued a long series of recommendations for modems at various speeds and for different applications. In addition to the scope of this report, our main interest is the category of modems from V.21 and higher. In the following sections a number of the most relevant normalized modem-standards will be discussed.

The CCITI-standards are indexed in V-series. The V-serie is a collection of protocols, established by the European P1Ts. Some of them relate to electrical prescriptions for transmission lines (V.l to V.19), most other known V-standards deal with modem protocols (approx. V.19 to V.37). Although the V-series had a relative late introduction, it has already passed by the American Bell-standards.

10.2 Overview or standardized modems

In this section different modem standards will be discussed briefly. The recom­ mendations are collected in the CCITI Blue Book. From the relevant recommen­ dations a selection was made that seems to be interesting in relation to the coding techniques discussed before. Generally the data rate, modulation and constellations will be described. Note that the V. recommendations do not provide any information about the (error)performances.

30 Recommendation V.21

300 bits per second duplex modem for use on the general switched telephone networks. Put into data transmission manually or automatically. Modulation: binary FSK

It-1080Hz, A-1750Hz Aj-lOOHu6Hz

Higher f corresponds to a binary O. f1 and f2 are respectively channel 1 and channel 2.

V.22

1200 bits per second duplex modem for use on the general switched telephone network (GSTN) and on point to point 2 wire leased telephone-type circuits.

-modulation: 2-DPSK each channel synchronous 600 baud -channel separation by frequency division Inclusion of scrambler and test facilities. - asynchronous, anisosynchronous

Carrier 1200 Hz ± O,5Hz low channel. Carrier 2400 Hz ± 1Hz high channel.

Datastream shall be divided into dibits. Each of the dibits shall be encoded as a phase change relative to the phase of the preceding signal element. The left of the dibit is the one first occurring in the datastream.

TABLE I/V.22

Dibil values Bit values Phase change Phase change (1200 bills' (600 bills) (Modes i, ii. iii. iv) (Mode v)

00 0 + 90" +270' 01 - 0' + 180" II I +270' + 90° 10 - + 180" 0°

"!ou ~ The phase change is (he actual on-line phase shift in the transition fClion from the centre of one signalhng element 10 the cenlrc of the following signaUins element.

31 V.22 his

TABLE I/V.n bis

2400 bits per second duplex modem using frequency division technique First two bits in quadbit (2400 bills) Phase standardized for use on the GSTN or dibit values (1200 bills) quadrant change and on point to point 2 wire leased telephone line. I~ 2 2~ 3 00 90° 3~ 4 4~ I

I~ I :! ---?>- :2 01 0" 3~ 3 -4-QAM for each channel at 600 baud 4~ 4 -2400 bps synchronous/asynchronous 1~4 2 ---?J- 1 -1200 bps synchronous/asynchronous II 270' 3~ 2 -carrier 1200 ± 0,5 2400 ± 1 Hz 4~ 3

I~ 3 2~ At 2400 bps the datastream is divided 4 0 10 180 3~ I into quadbits 4 ---?J- 2

Phase Quadrant 2 Phase Quadrant 1

11• 01• 10• 11•

10• 00• 00• 01•

-3 -I

01• 00• -I 00• 10•

11• 10• oJ 01• 11• [Cln·",.,o

Phase Quadrant 3 Phase Quadrant 4

FIGURE 2/V.22 b,s Signal con'll-nation

Figure 21

32 V.23

600/1200 bits per second modem standardized for use in the GSTN.

-FSK modulation synchronous, asynchronous

V.26 (bis/ter)

2400 bits per second modem standardized for use on 4 wire leased telephone circuits.

TABLE I/V.26

D· ••• -na l -110-

Phase change (see Note) -~ rJ f\ i f\ ! f\ D1bit r'J Alternali'w't A Ahernali'w't B V\T V'JJ\Jvv

00 0" +45" 01 +9Q" + 135" II + ISO" + 225" 10 + 270" + 315" CCITT"'J600 FIGURE I/V.26

NO/~ - The phase changc is the actual on·linc phase shin in the tfansition region from the centre of ont signalling clement 10 lhe centre of the following signllilini clement

-4-PSK, synchronous, 1200 bd -full duplex -inclusion of a backward supervisory channel 75 bd.

It should be noted that although recommendations V.26bis and V.26ter were developed later, there are no particular differences concerning to the applied coding techniques. There is a distinction according to answering and call operations as well as certain test procedures. However, these subjects are heyond the scope of view of this report.

33 V.27

4800 bits per second modem

TABLE I/V.27

Phas~ chang~ Tribil values

0 0 I 00 0 0 0 45° 0 1 0 90° 0 1 I 135 0 1 I 1 180° 1 1 0 225 I 1 0 0 no I 0 1 315' I

NOle - Th~ phase change is. the actual on-line phase shift in lhe' lransilion region from the centre of one !l.ignalling element 10 {he centre of the following signalling element

-8-DPSK synchronous, 1600 Bd -manual equalizer -backward channel 75 bd

34 V.29

9600 bits per second modem standardized for use on point to point 4 wire leased telephone-type circuits,

TABLE I "V.29 10'

45'

Phase change 02 04 OJ (see Note)

0 0 1 0' IIO'---_--~~~-""t---O· Absolute 0 0 0 45 0 I 0 90" 0 1 I 1)5' 1 1 I 180 22S' 1 1 0 225' CCITT ]4510 1 0 0 270' 270' I 0 I 315 FIGURE 21V. 29

NOll' - The pha!le change j!l the actual on-line phase :,>hifl in the transition region from the centre of one signalling element 10 the centre of the following signalling demt>nl.

TABLE 3/V.29 ., TABLE 2/V.29 Quadbits Dala bits Phase change 01 02 03 Q4

0 1 O' Relative signal e1emen! 0 0 0 0 Absolute ph~"e QI 90' amplitude 0 1 0 0 1 0 1 1 0 1 1 1 180' 0 J 1 0 0 1 0 0 270 0',90 . 180'.270' 1 5

r.; 0 \- 45'.1)5.225',3W I 3 12 90'

90' 5 180"---_---1r---~---O· Absolute 135'

------4If-7--"""'!~-"lSP-0- Absolute 270' con )4520

FIGURE J V.29

225' 315'

270' CCfTT·MMO FIGURE (IV 29 Slpo,_...... 0' _111,/.

35 -symbol rate 2400 Bd -fal1back rates 7200, 4800 bps -adaptive equalizer -data signal1ing rates

Fall back rates are selected if the channel condition requires a lower signa11ing rate.

9600 bps; 16-QAM 7200 bps; 8-QAM 4800 bps; 4-QAM (= 4-PSK)

V.32

2 wire duplex modems up to 9600 bits per second standardized for use on GSTN and leased lines.

-32-QAM at 2400 bd -data signalling rates 9600, 4800, 2400 bps synchronous -Trellis coding; R = 4/5, K=4 (or v=3)

SIgnat r------: ;------: element 0', I ,Y2,j I Y2, mapping lsee I See IV1~ : Yl,. Figure T..... 31V.32 2iV.32 ' 0' I Table 3/V.321 I, I I, I L- ---.J

I I Convolutional encoder b Symbol lruth 18ble a:m"l40C I ~ ...J • b , I~. 0 0 Differential encoder .-4-.5, 0 0 0 ,, 0 , 0 , 0 , , 0 ,

FIGURE 2/V.12

TrPllis codinl(.1 9600 bills

For 9600 bps; 16 input signals and 32 signals at decoder. The bit stream is divided into quadbits who are encoded in a trel1is encoder.

36 for 4800 bps; dibits are directly mapped into a 4-0AM constellation.

TABLE 2/V.32

Dine-mllal ftlrotIi.. for Uf with Ire-Ills C'Odtd Iltft1l8tin at 9600 bitfl

Inputs Previou!i OUlpulS Outputs

QI" Q2" YI" I Y2 n _ 1 YI" Y2"

() () 0 0 () () () () () I () I () () I () I 0 () 0 I I I I

() I 0 () () 1 () I I () I () () () I I 0 1 I () I 1 I I 0

I 0 0 0 I 0 I 0 0 I I I I 0 1 0 0 I I 0 I I 0 0 I I 0 0 1 I I I 0 I 1 () I I I 0 0 0 I I I I 0 I

llml 110· ":,,.r,,:.. 01~ @ OO~Ol 01~'0 10~O' 10~OO ,0:'0 2 i ,0:" ":oo O'~" 00:'0 O'~Ol @ OC:סס 110' -----..-- • ----.--- • ~ • ---,--- • -~,--4) O· IRe' -. "001 -2 ""0 I "0'0 2 11101 ,.

oo~, 1 0 01~)l oo~ 10 01~' 1 OO~oo ,0::00 ,o~ ,~21 ,0::0, ,o,~o 01~'0 00:0, ® o,~oo

11 ~~·1 "~Il can - "110 210

The blnarv numbers denote Y0l'l Y,!" Y2r. 03" Q4"

FIGURE J/V.J2

J2-poinl silnllll,...w", wUh trrilis (odina for 9600 hUls and slltts ABC () wMd It aoo bil is ••d for tnlnina

37 V.32bir

A duplex modem operating at data signalling rates of up to 14400 bits/s for use on the GSTN and on leased lines.

-duplex on GSTN and leased lines -channel separation by echo cancelling -128-QAM at 2400 bd at 14.000 bits/so -data signalling rates: 14.400 bits/s trellis coded 12.000 bits/s trellis coded 9.600 bits/s trellis coded 7.200 bits/s trellis coded 4.800 bits/s uncoded -backward compatibility with V.32 modems at 9600 and 48 bits/s

~, 0'" 14400 bit!s • '-, 050, 14400 ...d 12000 bit!s .. C!", 04,. 14400. 12000 and "00 bit!s .- w<" OJ., 14400. 12000. "00 and 7200 bit!s .- CJ~ 02" ~:",

01,., !l"

• ~ .. • '" c 0 0 1 1 c . ~

FIGURE ItV.32bis

In fact the recommendation V.32bis is an extension of V.32 with the same encoding structure. The data signalling rates of V.33 (up to 14400) bits/s) are combined with the duplex GSTN properties of V.32.

38 V.33

14.400 bits per second duplex modem for use on 4 wire leased telephone lines.

-128-QAM, 2400 Bd -fallback 12.000 bps -8 state trellis modulation, K=4, R =6/7 -symbol rate 2400 Bd

Signal element Mapping (Note) I I I I I I II Convolutional encoder L ~ SVmbols • b 5 5 Differential 0 0 0 0 encoder ·45, 0 1 1 0 1 0 1 0 ~=D-5, 1 1 0 1

Nolt - see FlIU~ 2{V.33 fot14 400 bitt. rate, Fillute 3/V.33 for 12000 blt/•.

FIGURE 1{V.33

TreIIiI coder.t 14 400 bitl. and 12 000 bill.

39 90" (1m)

0000110 000;110 5 • 000001l 1001111 0001011 10001lJ

1100100 1001010 IIlOI00t 1000010 1010100 ~ 1011101 110;001 1ll;101 t61lJ;001 • 1101101 1010001 "",,:""""",,,""00',,,'":"""•,;,,,"'r,,,;,,:":'" ",;",""'00"",,,"""'"00''' 1000100 1101010 0100100 0101010 0110100 0100010 00J0100 1100010 0000100

2 • • © • 0001101 1000001 0011101 0100001 0111101. t0110001. 0101101 0010001 1001101 0000001

0001000 IlJOll0 0011000 0110110 01lJ000 0111110 0101000 1111110 1001000

150" -8 1110011 -6 1111111 -4 0110011 -2 0111111 OIlJOll 0110111 Illl01l lllOlll r1' IRel

1001100 1111010 0101100 Olll010 0111100 0110010 0011100 1110010 0001100

• @. •• 2 • 0000101 1001001 0010101 0101001 Oll0101 t- 0111001 0100101 0011001 1000101 0001001 ... oooo,~"00':"''''"",,:" ~:,,'" :""" ,,,;,""F",;":""" '"'":'0000'""",'""","" ,:oo~'

1011010 1101100 0011010 1111100 0010ul0 1011100 1010010 6 1010101 1101001 1110101. t- lll1001.• ®1100101 . • 1011001

1010000 1000110 l110000 1001110 1100000 1000011 0001111 t-5100;011 • OOO'Olll 0001010 0000010 7/r1' T17000IH'

Binary numbers refer to 06n. OSn. 04n. OJn. Y2 n. Y1 n. YOn. A. B. C. 0 refer to synchronlzmg lignaI element5

FIGUR~ 2!V.))

SipaJ JPace diapam UMI mappina ror trellil'"'COded modulation at 14400 bitJ.

40 11 Recent technical developments

So far, we discussed the standardized coding techniques. Recent research has already led to improved designs. Some of them are already applied into commercial availahle modems. The greater part however is still in an experimental stadium. It is expectable that a number of these experimental designs will be proceeding for new modems and recommendations.

In the following sections, recent developments will be discussed. The subjects are grouped by their technical properties. Generally it involves improvements on coding techniques and principles in order to achieve 19.200 bits/s duplex on 2 and 4-wire telephone channels.

11.1 Multicarrier Modulation

This approach borrows from communications technology used by the military in secure communication systems. [Humphrey] This technology breaks data into discrete pieces and spreads them across the available bandwidth on separate carrier frequencies, keyed at different time intervals The basic idea of multicarrier modulation (MCM) is to achieve data rate on a noisy, distorted channel by dividing the channel into different pass-bands. As a subse­ quence, different carriers are used. If a channel is distorted, only certain parts of the band will be used. The advantage of this approach is it's ahility to "map around" bad spots in telephone lines.

Input data at ms fs bits/s are grouped into blocks of M bits at a symbol rate of fs' mn bits for the carrier at fc•n to modulate Nc carriers, which are spaced of apart across any usable frequency band.

The modulated carriers are summed for transmission, and must be separated in the receiver. Several methods have been used for this and demultiplexing in the pa~t, but the preferred method is now to key the carriers using OASK. (for a more complete introduction see [Bingham])

11.1.1 Applications

Multicarrier modulation is applied in the Packetized Ensemble Protocol (PEP). This is not an official standard. PEP is used in high speed (up to 9600 bits/s) modems from Telebit, and Ventel [Humphrey].

[Hirosaki] describes a 19.2 kbit/s modem based on orthogonally multiplexed QAM techniques in which the entire transmission band is divided into a number of mutually spectrum overlapping sub-channels. The design differs frQm conventional modems in that it uses out-of-band pilot tones for stahle carrier and clock frequency control.

[Telebit]

41 11.2 Multilevel coding

Multilevel coding is an approach to achieve higher coding gain by extending the encoding function.

In a conventional trellis coder, in for example the V.32 modem, the bitstream is divided into blocks of 6 bits. Bit 1 and 2 are encoded in a convolutional encoder. The parallel bits are then sent directly to a mapping device.

In a multilevel encoder the parallel bits are coded by more than one coder (block or convolutional) before they map the signal points.

:i ~ f-----~------">I " r------~ 3: • • f------3>I .. ~ 'f------3>I "

(a) Conventional 2-D trellis coded modulation

~ '"'0 . ; ..3: , 0 " ~ " E 3 . E 2 E I (b) Conventional 2-D multilevel coded modulation [ Eo: encoder of a one-level code]

Figure 28

More about block codes can be found in [de Bot]

11.2.1 Applications

[Ushirokawa] describes a scheme with competItive performance related to conventional trellis codes for a 19.000 bits/s voiceband modem. Compared to 2-D and 8-D TCM, multilevel coding showed an improved total performance by achieving higher coding gains and shorter decoder delay.

A SiN of 25 Db was achieved at a bit error rate of 10-6.

11.3 Advances in trellis-coded modulation

[Motorola] At the time of the formulation of recommendation V.32 in 1983-84, trellis-coded modulation was quite new. The 8-state, two-dimensional code adopted in V.32, V.33 and V.32his was the state of the art at the time. A number of new classes of trellis codes suitable for high numbers of bits per symbol have been developed since 1984. Compared to the Ungerboeck-type codes, the new

42 developed codes do not achieve much improvement on the performance vs. complexity trade-off. So a more complex constellation with more signal points to map requires a more complex encoding and decoding mechanism. A higher complexity will reduce the signal processing rate.

11.3.1 Multidimensional trellis coding

An approach to handle the problem of constellation complexity is to convert the dimensional constellation into a multidimensional constellation. Multidimensional trellis coding is an efficient new coding scheme which can achieve large coding gain without increasing the number of constellation points. In this coding, encoded data with one redundant bit is mapped onto a multi-dimensional signal consisting ofseveral consecutive two-dimensional signals, thus reducing the size of the signal constellation. This reduces the degradation caused by the dense signal constellation based on the usual two dimensional coding scheme.

Comparison 8 bit 2-dimensional vs. 32 bit 8-dimensional

These constellations are interesting to compare because the 8 dimensional (8-D) constellation is a quadruple extension of the 2-D signal set.

8 bit 2-D +1 bit redundant (3dB loss resulting from the doubling of the number of points in the same signal space

256-QAM (8 bit) ---> 512 QAM (9 bit) (coding gain 6dB)

32 bit 8-D + 1bit redundant 0.75 dB loss (3dB/4)

(256_QAMt(8-dimmsional) (32 bit)(8-D) ---> 8.56109 points (33 bit) (4.5dB coding gain)

--- > (304 QAM)4 (8-dimensional) 33 bit 8-D

Compared to one 512 QAM constellation, multidimensional trellis coding reduces constellation expansion. Multidimensional coding has been further developed by [Wei].

11.3.2 Applications

In 1985 Codex introduced 19.2 kb/s modem in which a 64 state 8D Wei code was implemented [Motorola].

[Tanaka] discusses the development of a 19.2 Kb/s modem based on eight dimen­ sional trellis coding. A SIN of 30 dB was measured at a bit error rate of 10-6 (26.2 5 Db at 10- ).

11.4 Shaping

Shaping can be recognized as an aspect of coded modulation systems that can be treated separately from coding. [Motorola]

43 The basic idea behind shaping is to optimize the shape of the constellation, in order obtain a maximum number of constellation points in a constellation with a maximum space in between. For example, the V.32, V.33, and V32his signal constellations are 2D 'cross constellations', which have a nominal 'shape gain' of about 0.14 Db over square QAM constellation. In principle, spherically shaped constellations are optimum. For a more fundamental discussion the reader is referred to [Calderbank].

An extension from this principle is trellis shaping where convolutional codes and trellis structures are used to realize a constellation partitioning.

11.5 Adaptive bandwidth

[Motorola] This approach is comparative to the multicarrier approach. Adaptive bandwidth concerns with achieving reliable operation at higher data rates with the use of maximum bandwidth available on individual GSTN circuits. For a new standard Motorola recommends different symbol rates (2400, 2743 and 3200 Bd) allowing fallback to slower V.rates.

11.5.1 Trellis precoding

[Motorola] Trellis shaping and equalization are combined in a technique called trellis precoding. Equalization is required to achieve minimum Inter Symbol Interference. With trellis precoding Codex obtained a datarate of 24 Kb/s in a commercially modem.

44 12 Current high speed modems

At this moment the latest modem designs achieve greater performance with advanced techniques described in the chapters before. In order to get an impression of state of the art (commercial) designs, some documentation of recent modem models was collected. However, a lot of the commercially brochures provided only superficial information. The greater part of information was restricted to Baudrate and modulation principles. In the next section the most interesting modems will be briefly discussed referring to the available documentation.

12.1 Summary

Fujitsu M1928L

19,200 bps modem Full duplex, synchronous, bit serial data transmission

Line requirement: voiceband, 4 wire, conditioned. Modulation: 16 state, 8 dimensional Trellis-coded QAM. Baudrate: 2743 Hz

Carrier Frequency: 1900, 1850, 1750, 1700 ± 1 Hz. Automatic adaptive equalization.

Gandal'DMl92 [Gandalf] 19,2 Kbps modem

Line requirement: voiceband, 4-wire leased line Modulation: Trellis-coded QAM 'constant simulated controlled carrier'.

SIR for BER = 10-6 at 19,2 Kbps: -3OdBm

Telebit 1'2500 [Telebit] Modem using PEP-protocol (see section 12.1.1) achieving 18.000 bps over two wire unconditioned leased lines.

Telsat 19250 [Baudoin] 19.2 Kbps modem Baudrate 2742.86 Hz (i.e. 8/7 of 2400 Hz) Modulation: Multi (8) dimensional Trellis coded modulation 16 state trellis encoder, rate 3/4 Coding gain is 7.83 Db with respect to an equivalent modem at 19.2 Kbps without coding at 2400(!)Bd. A BER of 10-6 was achieved at a SIR 27 dB and 19.2 Kbps (coded).

Racal-Milgo Omnimode 1614

45 [RacaI1] 16.8Kbps modem Modulation: (2-dimensional) 'Racal-Milgo' 256 point trellis coded modulation at 2400 Bd

Racal-Milgo Excalibur 19.2 [RacaI2] 19.2 Kbps modem over 4-wire leased lines. Modulation: multidimensional trellis coding

Codex 3385 [Codex1] 19.2 Kbps modem based on a Codex chip set, a 68000 microprocessor and two TCM­ schemes.

Modulation: Multidimensional Trellis Coded Modulation

'Line Quality Adjustment' Two user-selectable TCM schemes that offer different coding complexity. Selecting depends on the line quality. 'Adaptive Rate System' Continuous line monitoring in order to maximize data throughput (fallback and fall forward data rates).

Codex 3600 Series Communication Platform [Codex2] 24 Kbps over 4-wire operating mode baud rates up to 3200 Bd

Modulation: Multidimensional Trellis Coded Modulation with Trellis Precoding

12.2 Notes

Data rates at 14.4 Kbps up to 19.2Kbps are achieved with multidimensional Trelliscoding in the greater part of the discussed modems. Combined with an increased symbol rate of 2743 Bd, this technique seems to become a de-facto standard in high speed modems. Extremely high performance achieved by the Codex 3600 model requires state of the art techniques like Trellis Precoding discussed in section 12.5.1. together with a symbolrate of 3200 Bd.

On the next page, a table is shown of the current available high speed voice-band modems.

46 Specifications of voiceband modems.

YFAR MODEL BIT RAND n CON- CODING COM- CCIT RATE W. srEL- MENfS (AnON (bps) (117)

1962 Bell 201 2400 1200 2 4-PSK V.26

1967 Racal-Milgo 4800 1600 3 8-PSK V.27 4400/48

1971 Codex 9600 C 9600 2400 4 If>.OAM V.29 ('76)

1976 9600 2400 4 If>.OAM V.29

1980 Paradyne 14.400 2400 6 64-QAM rectan- MPI4400 gular

1981 Codex SPI4.4 14.400 2400 6 64-QAM hexagonal

1984 9600 2400 5 32-QAM 8-stale (2/3) V.32 Trellisroder GSTN

:!: 1987 Fujilsu MI92RL 19.200 2743 29 (160- 16 slale leased QAM)4 Trellisroder line

1989 Telsal 19250 19.200 2743 29 (160- leased QA~)4 line

:!: 1989 Telebit T2.';00 18.000 Multi- carrier- transm.

1988 14.400 2400 7 128- 8-slale (2/3) leased V.33 QAM Trelliscoder line

1990 14.400 2400 7 128- 8-state (2/3) GSTN V.32bis QAM Trellisroder

:!: 1989 Racal-Milgo 16.ROO 2400 8 25&- TreIIiscoded leased Omnimode 1614 QAM line

:!: 1987 Codex 19.200 2743 29 Multi dim. leased 3385 dalamodem TCM line

:!: 1990 Codex 3600 24.000 3200 Multi dim. communications TCM plalform Trellis preroding References

[Baudoin] G. Baudoin and M.S. Mitrani. Telsat 19250: 19200 bit/s leased line modem. Commutation & TransmL'ision NQ 2, 1989

[Bingham]John A.C. Bingham. The theory and practice ofmodem design. John Wiley & Sons, New York

[de Bot] P.G.M. de Bot. Design of a Digital Communication System using Multistage Block Coded Modulation. Technical Report, Eindhoven University of Technology, Eindhoven, The Netherlands, March 1991. (to appear)

[Calderbank] A.R. Calderbank. The Mathematics of Modems. Preprint from a publication in the Mathematic Intelligencer. august 1989.

ICCITTl CCITTBlue book. Volume VIII· fascicle VIII.1 Datacommunications over the telephone network. series V recommendations. International Union, Geneva, 1988

[Codex1] Codex Corporation. Documentation Codex 3385 Data Modem. 1670/103­ 20M-1-90. Mansfield, MA 1990

[Codex2] Codex Corporation. Documentation Codex 3600 Series Communication Platform. 1670/104-20M-4-90. Mansfield, MA 1990

[Forney et all G.D. Forney, R.G. Gallagher, G.R. Lang, F.M. Longstaff and S.U. Qureshi. Efficient Modulation for Band-Limited ChannelsJEEE Journal on Selected Areas in Communications, VOL SAC-2, pp. 632-647, september 1984

[Fujitsu] Fujitsu Limited. Documentation Fujitsu M1928L 19.2 Kbps Modem (11/87)

[Gandalf] Gandalf Nederland BV. Documentation GandalfDM192 Modem. NL89/1

[General Datacom] General Datacom, Inc. Coding Scheme for Two- Wire Full Duplex 19,200 bitls Modem. CCITT study group XVII. Delayed Contribution D79. Geneva, October 1990.

[Haykin] S. Haykin. Digital Communications. John Wiley & Sons Inc, New York

[Hirosaki] B. Hirosaki et al. A 19.2 Kb/s voiceband data modem based on orthogonally multiplexed QAM techniques. In Proc. of IEEE Int. Conference on Communications '85, pp. 21.1.1-21.1.5, Chicago, June 1985

[Humphrey] J.H. Humphrey and G.S. Smock. High-Speed Modems. BYTE june 1988.

[Motorola 1990] Motorola Information System Group. Advances in modem tee/mologr since recommendation ~32. CCITT study group XVII. Delayed Contribution D92. Geneva, October 1990.

48 [Proakis] J.G. Proakis. Digital Communications. McGraw-Hill, Singapore, second edition, 1989.

[Racal] Racal-Milgo.Documentation Racal-Milgo Omnimode1614Modem Publication No RML19-A(6/89)

[Sklar] B. Sklar. Digital Communications. Prentice and Hall Computing

[Tanaka] Y. Tanaka et al. A 19.2 Kb/s high speed voiceband data modem on eight state trellis coding. In Proc. of IEEE GLOBECOM '87. pp. 36.1.1-36.1.5, Tokyo, November 1987

[Telebit1] Telebit Corporation. A Tutorial on Multicarrier Modulation for GSTN modems. CCITT study group XVII. Delayed Contribution 081 rev. Geneva, October 1990

[Telebit2] Telebit Corporation. Documentation Telebit T2500 Standalone Modem. 3/89 P/N90093-01

[Ungerboeck] G. Ungerboeck. Channel Coding with multilevel/phase signals. IEEE Trans. Infonnation Theory, IT-28(1):55-67, january 1982.

[Ushirokawa] A. Ushirokawa and H. Matsui, Multilevel Codes for High-Speed Voiceband Data Modem. In Proc. of IEEE GLOBECOM '89, pp. 54.7.1 Dallas, 54.7.1, Nov. 1989

[Wei] LF. Wei, Trellis-coded modulation with multidimensional constellations. IEEE Trans. Infonn. Theory vol IT-33. pp. 483-501. 1987

49 A Glossary Of Notations dmin minimum Euclidean distance ~ energy per bit Ell energy per signal G.. asymptotic gain I, J integer counters K constraint length m number of bits per coded signal M number of N number of dimensions of a signal set n code length P probability R code rate s signal v constraint length of a convolutional encoder

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