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Trellis-coded modulation forvoiceband data modems

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A Doctoral Thesis. Submitted in partial fulfilment of the requirementsfor the award of Doctor of Philosophy at Loughborough University.

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LOUGHBOROUGH UNIVERSITY OF TECHNOLOGY

LIBRARY

AUTHOR/FILING TITLE

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ACCESSION/COPY NO.

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003 2810 02

~~IIIIIII~III\IIII~I\II\\II\III\\I~~III\III .

TRELLIS-CODED MODULATION FOR

VOICEBAND DATA MODEMS

by

SHU FUN ALEXIS lP, B.Sc., M.Sc.

A Doctoral Thesis

Submitted in partial fulfilment of the requirements for the award of

Doctor of Philosophy

of the LoughboroughUniversity of Technology

September 1988

Supervisor : Professor Adrian Percy Clark

Department of Electronic and Electrical Engineering

~ by S. F. A. lp, 1988

ABSTRACT

The thesis is concerned with a combined convolutional coding and

modulation technique, known as Trellis-Coded Modulation (TCM), with AM and

QAM signals. TCM provides a useful error correction capability, without

bandwidth expansion, by increasing appropriately the number of possible

levels in a transmitted signal element. The development of the

Correlative-Level Modulo Arithmetic (CLMA) coding technique has opened up

a new approach to the understanding and implementation of TCM. The study

goes further in optimizing the performance of the CL MA coder by

investigating various combinations of the correlative-level coding vectors

and the modulo arithmetic operations. A new CLMA coding technique is also

studied for the coding of a 16QAM signal. A further application of modulo

arithmetic is then investigated for Ungerboeck's convolutional codes. An

equivalent set of codes using the CLMA coding technique is obtained for

Ungerboeck's rate 1/2, 2/3 and 4/5 convolutional codes with multilevel

signals. Rate 4/5 90 degree and IBa degree 32QAM rotationally invariant

codes are next introduced and simulated using a novel technique that

involves the application of an adaptive CLMA coding scheme. A new set of

optimum IBa degree rotationally invariant codes is also developed, and

these are complemented by an automatic 90 degree phase correction

technique. Performances of codes using a Viterbi-algorithm decoder and

various near-maximum-likelihood decoders are studied in the thesis. The

most cost-effective decoder needs only a fraction of the equipment

complexity required by the corresponding maximum-likelihood decoder. It

therefore allows the use of convolutional codes with a long constraint

length, which have a better asymptotic coding gain than shorter codes. The

systems studied are suitable for ,data modems transmitting at rates up to

9600 bit/so Computer simulation test results are presented for the

comparison of the relative tolerances to white Gaussian noise of various

systems.

i

ACKNOWLEDGEMENTS

I would like to express my deepest gratitude to Professor Adrian Cl ark for his constant and enthusiastic encouragement of the research project. His

superb supervision and most professional approach, in every way, has

benefited me tremendously. I would also like to thank CASE Communication

Ltd. and Professor Cl ark for their financial support which made the

completion of the project possible.

I would also like to thank my christian brothers and sisters in

Loughborough for supporting me, both in prayers and in actions, during the

preparation of the thesis.

Much gratitude must go to my wife, Kwen, who has persevered so much in

every way. Without her daily support and exhortation, the completion of

" the thesis would not have been possible.

Finally, I would like to express my gratitude towards my parents for their

hard work and patience in assisting me in my education and career.

ii

LIST OF PRINCIPAL SYMBOLS

ai = binary data symbol at the input to the data-transmission system (eqn.2.l6)

a = input binary data symbol when separated into groups of j ~,J

symbols {ail (eqn.2.l7)

Ci = cost of a stored vector obtained after the receipt of ri in a decoder (eqn.2.50)

ci = incremental cost of a stored vector after the receipt of ri in a decoder (eqn.2.51)

dist(x,y) = Euclidean or Unitary distance between sequence x and sequence y (eqns.2.53 and 2.54)

duncoded - E[.]

f( )

G

g

= minimum free distance of a code (eqn.2.55) = normalized minimum free distance of a code(eqn.2.56) = normalized minimum distance of an uncoded system (eqn.2.5B) = expected value or mean value = average transmitted signal energy per symbol = average transmitted signal energy per bit = recoded symbol of a stored vector in the decoder after the

receipt of ri (eqn.2.47)

= coded signal mapping function = semi-infinite convolutional code generator matrix (eqn.2.22) = asymptotic coding gain over an uncoded system (eqn.2.59) = convolutional code generator matrix of polynomials of

Delay-operaters (eqn.2.27)

= number of symbols (or sampling intervals) involved in the memory of a code

g+l = constraint length of a code gb = effective number of bits in the code memory H = semi-infinite parity-check matrix (eqn.2.33) H(D) = parity-check matrix of polynomials of Delay-operators

Im[.]

j

K

m

(eqn.2.36)

= the imaginary part of a complex number = ~ (when not being used as subscript) = number of possible values of si (eqn.2.l4) = number of stored vectors in a decoder

Hi

m MOD(N)

n

= average number of stored vectors in a decoder

= a function that defines a set of operations involving the use

of real modulo-N arithmetic (eqn.3.9)

= delay in decoding (measured in number of data symbols)

N' = number of data symbols in the sequences used for

measuring the dfree (eqn.2.55)

No/2 = two-sided power spectral density of the zero mean stationary

AWGN added at the input to the receiver filter

= expanded vectors that derived from a Zi_l in a decoder

= average probability of bit errors in a decoding process.

= Q-function (eqn.2.4)

qi

ri Re[.]

Si

si 1

wi y

Zi

= transmitted coded symbol

= received signal sample at time t=iT

= the real part of a complex number

= state of a coder at time t=iT (eqn.2.40)

= K-Ievel uncoded data symbol

= sampling interval

= additive white Gaussian noise (AWGN) component

= coding vector in a CLMA code

= stored vectors (sequences) in a decoder

in

v = number of information bits per sampling interval ~ = number of coded bits per sampling interval

a 2 = variance of the real-valued noise component wi

ri

f = signal-ta-noise ratio (SNR) (eqn.2.60 and eqn.2.6I) o(t) = unit impulse function (dirac function)

1.1 = modulus or absolute value

iv

CONTENTS

Abstract

Acknowledgements

List of Principal Symbols

CHAPTER 1 Introduction

CHAPTER 2 : Basic Assumptions

2.1 Model of Binary or Quarternary Uncoded

Data-Transmission System

2.2 Model of a 16QAM Uncoded Data-Transmission System

2.3 Model of a Data-Transmission System Using

Trellis-Coded Modulation (TCM)

2.4 Convolutional Coding and Signal Mapping Process

2.5 Viterbi-Algorithm Decoding

2.6 Minimum Free Distance and Asymptotic Coding Gain

2.7 Computer Simulation Tests

CHAPTER 3 Correlative-Level MOD(N) Coding of Quarternary

Baseband Signals

3.1 Model of the Data-Transmission System

3.2 Quarternary Correlative-Level MOD(N) Coder

3.3 Code-Search Procedures for Correlative-Level

MOD(N) Codes

3.4 Correlative-Level MOD(N) Codes with Coding Memory

3.5 Viterbi-Algorithm Decoding of Correlative-Level

MOD(N) Codes

3.6 Correlative-Level MOD(N) Codes with Coding Memory

3.7 Near-Maximum-Likelihood Decoding Processes

3.7.1 System-l

3.7.2 Pseudobinary System-A

g=2

g>2

Page

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Hi

1

9

9

16

20

23

31

34

37

39

39

41

44

45

63

74

84

84

102

Page

CHAPTER 4 Correlative-Level Modulo Arit