Collaborative coding multiple access communications

warwick.ac.uk/lib-publications

A Thesis Submitted for the Degree of PhD at the University of Warwick

Permanent WRAP URL:

http://wrap.warwick.ac.uk/110301

Copyright and reuse:

This thesis is made available online and is protected by original copyright.

Please scroll down to view the document itself.

Please refer to the repository record for this item for information to help you to cite it.

Our policy information is available from the repository home page.

T H E B R IT IS H L IB R A R Y

BRITISH THESIS SERVICE

TITLE

Collaborative Coding Multiple Access Communications

A U T H O R

Falah H assan Ali,

D EG REE...

A W A R D IN G BODY

D A T E ...

^ v e r s W O ^ a r - c V

iqqa

THESIS

NUMBER

T H I S T H E S IS H A S B E E N M IC R O F IL M E D E X A C T L Y A S R E C E IV E D

The quality of this reproduction is dependent upon the quality of the original thesis

submitted for microfilming. Every effort has been made to ensure the highest quality

reproduction.

Some pages may have indistinct print, especially if the original papers were poorly

produced or if the awarding body sent an inferior copy.

If pages are missing, please contact the awarding body which granted the degree.

Previously copyrighted materials (journal articles, published texts, etc.) are not

filmed.

This copy o f the thesis has been supplied on condition that anyone who

consults It Is understood to recognise that Its copyright rests with Its author

and that no Information derived from It m ay be published without the

author's prior w ritten consent.

Reproduction of this thesis, other than as permitted under the United Kingdom

Copyright Designs and Patents Act 1988, or under specific agreement with the

copyright holder, is prohibited.

L J . ' I

1 2

” T 3

REDUCTION

Collaborative Coding Multiple Access Communications

By

Falah Hassan A li, B.Sc., M.Sc., AM IEE

A T hesis Submitted fo r the D egree o f

D octo r o f Philosophy

U n iversity o f W a rw ick

Department o f Engineering

June 1992

Table o f Contents

T itle P age

T a b le o f C on ten ts

L ist o f F igu res and Tables

A ck n o w ledgm en ts

Declarations

Abstract

Chapter 1: Introduction

Chapter 2: In trod u ctio n to M u ltip le A ccess Communications

2.1 Introduction

2.2 M u ltip le A c c e ss Channel

2.3 M u ltip le A c c e ss Techniques

2.3.1 F requ en cy D ivisio n M u ltip le Access (F D M A )

2 .3.2 T im e D ivision M u ltip le Access (T D M A )

2.3.3 C o d e D ivision M u ltip le A ccess (C D M A )

2 .3.4 C o lla b o ra tiv e C o d in g M u ltip le A ccess (C C M A )

2.4 M u ltip le A c c e ss Channel M odels

2.5 M u ltip le A c c e ss Inform ation Th eory

2.6 M u ltip le A c c e ss C oding/D ecoding Techniques

i l l

i

iii

v iii

x v i

x v ii

2.6.1 C o d e Constructions fo r N oiseless Channel 29

2.6.2 C o d e Constructions fo r N o is y Channel 33

Chapter 3: In form a tion Transmission C apacity o f Sin gle A ccess C han nel 37

3.1 Introduction 37

3.2 T h eo retica l Basis and D evelopm en t o f Channel C apacity 38

3.2.1 Unconstrained Channel 39

3.2.2 Constrained Channel 41

3.3 IS A / O S C Constrained Capacity 47

3.4 IS A P / O S C Constrained Capacity 52

3.5 Sim ulation Results and Discussions 53

Chapter 4: In form a tion Transmission C apacity o f M ultiple A c c e ss Channels 68

4.1 Introduction

68

4.2 T -u ser M u ltip le A ccess Com munication System

68

4.3 M o d e llin g o f T-u ser M -ary A d d e r Channel 71

4.4 M o d e llin g o f T-u ser M -ary Frequency Channel 77

4.5 M u ltip le A c c e ss Capacity 84

4.5.1 N o is e les s Channel 8 7

4.5.2 N o is y Channel

88

4.6 Sim ulation Results and Discussions 91

4.6.1 C ap acity o f T-user M -a ry A d d er Channel 93

4.6.2 C a p a city o f T-u ser M -a ry Frequency Channel 99

2.6.1 Code Constructions for Noiseless Channel 29

2.6.2 C o d e Constructions fo r N o isy Channel 33

Chapter 3: In form a tion Transm ission Capacity o f S in gle A ccess Channel 37

3.1 Introduction

37

3.2 T h eoretical B a s is and D evelopm ent o f Channel Capacity 38

3.2.1 U n constrained Channel

39

3.2.2 C onstrain ed Channel

4 1

3.3 IS A /O S C C onstrain ed Capacity 47

3.4 IS A P / O S C C onstrained Capacity 52

3.5 Sim ulation R esu lts and Discussions

53

Chapter 4: In form a tion Transm ission Capacity o f M u ltip le A ccess Channels

68

4.1 Introduction

68

4.2 T -u ser M u ltip le A ccess Com munication System

68

4.3 M o d e llin g o f T -u s e r M -ary A d d er Channel 71

4.4 M o d e llin g o f T -u s e r M -ary Frequency Channel 77

4.5 M u ltip le A c c e s s Capacity 84

4.5.1 N o is e le s s Channel 87

4.5.2 N o is y Channel

88

4.6 Sim ulation R esu lts and Discussions 91

4.6.1 C a p a c ity o f T-user M -a ry A d d er Channel 93

4.6.2 C a p a c ity o f T-user M -a ry Frequency Channel 99

Chapter 5: C o lla b o ra tive Coding/D ecoding M u ltip le A ccess Techniques 103

5.1 Introduction 103

5.2 T -user E n co d in g T ech niqu es 103

5.3 T -user D e c o d in g T ech niqu es 107

5.3.1 H ard D e c isio n (H D ) D ecod in g 108

5.3.2 M a x im u m Lik elih o o d S o ft D ecisio n (M L S D ) D ecodin g 109

5.4 L o w C o m p le x ity M L S D _ C C M A D ecod in g 111

5.4.1 D e c o d in g Procedure D escription 112

5.4.2 D e c o d in g A lgorith m 113

5.4.3 2-user M L S D _ C C M A D ecod in g Schem e 114

5.5 E rror P ro b a b ility A n alysis 117

5.5.1 S y m b o l E rror Probability 117

5.5.2 S y m b o l E rror Probability M inim isation 120

5.5.3 C o d e w o r d Error Probability 121

5.5.4 2-user C C M A D ecod in g Schem es Error Probability 124

5.6 Sim ulation R esu lts and Discussions 126

Chapter

6

6.1 Introduction 138

6.2 M od em T ech n iq u es Considerations 138

6.3 M F S K .C C M A M o d e m M o d e l 140

6.4 S q uare-Law D em odu lation T ech niqu e 143

6.5 Zerocrossing D em odu lation T ech niqu e 146

6.6

6.7 2-user M F S K _ C C M A System D evelo p m en t 157

6.8

6.8.1 M od em s O p era tion V erifica tio n 159

6.8.2 A W G N C h a n n el Tests 159

6.9 Discussions 162

Chapter 7: C onclusions and Further W o rk 166

7.1 Conclusions 166

7.1.1 Inform ation C apacity o f Constrained S A C 166

7.1.2 Inform a tion C apacity o f M A C s 167

7.1.3 C o lla b o ra tiv e Coding/Decoding M ultiple Access Techniques 168

7.1.4 Practical C C M A M odem D esign 168

7.2 Further W o rk 169

7.2.1 O ptim isa tion o f Channel C apacity 169

7.2.2 Im proved C o lla b o ra tive Coding/Decoding Designs 171

7.2.3 A d a p tive C C M A Transmission System 172

7.2.4 M u lti-Fu nctional Signal D esign Format 173

R eferences 176

S ym bols and Abbreviation s 196

A p p en d ix A : C onditional P ro b a b ility Density Function for Quantised

A W G N C h an n el Output 201

Appendix B: Symbol Error Rate for 2-user Binary C CM A Scheme 202

Appendix C : C o d ew o rd E rror R ate Em ployin g H D D ecod in g

fo r 2-user B in a ry C C M A Schem e 205

A ppendix D : C o d ew o rd E rror R ate Em ployin g M L S D Decoding

fo r 2-user B in a ry C C M A Schem e 211

List o f Figures and Tables

F igu re 2.1 M u ltip le A ccess C om m un ication Channel 9

F igu re 2.2 C lassificatio n o f M u ltip le Access C om m un ication 9

F igu re 2.3 C lassificatio n o f M u ltip le A ccess M ethods 12

F igu re 2.4 Frequ en cy D iv is io n M u ltip le Access 13

F igu re 2.5 T im e D ivisio n M u ltip le A ccess 14

F igu re 2.6 C o d e D ivisio n M u ltip le A ccess 15

F igu re 2.7 C lassificatio n o f D iscrete Input M A C s 19

F igu re 2.8 2-user N oiseless B in ary A d d e r M A C M o d e l 20

F igu re 2.9 2-user N oiseless B in a ry O R M A C M o d e l 21

F igu re 2.10 2-user N oiseless B in a ry E xclu sive-O R M A C M od el 22

F igu re 2.11 2-user N oiseless B in a ry A N D M A C M o d e l 23

F igu re 2.12 2-user N oiseless B in a ry Sw itching M A C M o d e l 2 4

F igu re 2.13 C a p a city R egio n o f 2-user M A C 26

F igu re 2.14 T -u s e r N oiseless B in ary A d d er M A C M o d e l 2 9

F igu re 2.15 T -u s e r N o is y B inary A d d e r M A C M o d e l 33

F igu re 3.1 C han nel Capacity versus S N R fo r B inary Input A W G N

C han nel (w ith T w o E quiprobable M ass Poin ts) 4 6

F igu re 3.2 Constrained C apacities as a Function o f Input Signal

A m p litu d e 5 4

Figure 3.3 Constrained Capacities as a Function o f Normalised SNR (dB) 55

57 F igu re 3.4a Optim um M ass P oin ts Distribution o f IS A /O S C C om trainti

W ith A = 1 .0 and S C =6.0

F igu re 3.4b Optim um M ass P oin ts Distribution o f ISA /O S C Constraints

W ith A = 1 .5 and S C =6 .0 57

F igu re 3.4c Optim um M ass P oin ts Distribution o f IS A /O S C Constraints

W ith A = 2 .0 and S C =6 .0 57

F igu re 3.4d Optim um M ass P oin ts Distribution o f ISA /O S C Constraints

W ith A = 2 .5 and S C = 7 .0 57

F igu re 3.4e Optim um M ass P oin ts Distribution o f ISA /O S C Constraints

W ith A = 3 .0 and S C = 7 .0 58

F igu re 3 .4 f Optim um M ass P o in ts Distribution o f IS A /O S C Constraints

W ith A =4 .0 and S C =8 .0 58

F ig iire 3.4g Optim um M ass P oin ts Distribution o f ISA /O S C Constraints

W ith A = 5 .0 and S C =9 .0 58

F igu re 3.4h Optim um M ass P oin ts Distribution o f ISA /O S C Constraints

W ith A = 6 .0 and S C =1 0 .0 58

F igu re 3.5a Optim um M ass P oin ts Distribution o f IS A P / O S C Constraints

W ith A = 1 .0 and S C =6 .0 59

F igu re 3.5b Optim um M ass P oin ts Distribution o f IS A P/O S C Constraints

W ith A = 1 .5 and S C =6 .0 59

F igu re 3.5c Optim um M ass P oin ts Distribution o f IS A P/O S C Constraints

W ith A = 2 .0 and S C =6 .0 59

F igu re 3.5d Optim um M ass P oin ts Distribution o f IS A P/O S C Constraints

W ith A = 2 .5 and S C = 7 .0 59

W it h A = 3 .0 and S C = 7 .0 60

Figure 3 .5 f O p tim u m Mass Poin ts D istribu tion o f IS A P/O S C Constraints

W it h A =4.0 and S C = 8 .0 60

Figure 3.5g O p tim u m Mass Poin ts D istribu tion o f IS A P/O S C Constraints

W it h A = 5 .0 and S C = 9 .0 60

Figure 3.5h O ptim u m Mass P oin ts D istribu tion o f IS A P / O S C Constraints

W it h A = 6 .0 and S C = 1 0 .0 60

Figure 3.6 O ptim u m O S C A s a F u n ctio n o f Norm alised S N R (d B ) 62

Figure 3.7a Output P D F o f IS A / O S C Constraints

W it h A = 1 .0 , S C = 5 .0, M = 2 , and S N R = 0 d B 63

Figure 3.7b Output P D F o f IS A / O S C Constraints

W it h A = 1 .5 , S C = 6 .0. M = 2 , and S N R = 3 .5 2 2 d B 63

Figure 3.7c Output P D F o f IS A / O S C Constraints

W it h A = 2 .0 , S C = 6 .0, M = 3 , and S N R = 5 .3 7 7 d B 63

Figure 3.7d O utput P D F o f IS A / O S C Constraints

W it h A = 2 .5 , S C = 7 .0, M = 3 , and S N R = 6 .7 8 3 d B 63

Figure 3.7e O utput P D F o f IS A / O S C Constraints

W it h A = 3 .0 , S C = 7 .0, M = 4 , and S N R = 8 .0 6 2 d B 64

Figtire 3 .7 f Output P D F o f IS A / O S C Constraints

W it h A =4.0, S C =8 .0, M = 4 , and S N R = 9 .9 9 5 d B 64

Figure 3 .7g Output P D F o f IS A / O S C Constraints

W it h A = 5 .0 , S C = 9 .0, M = 5 , and SN R = 1 1.5 4 3 dB 64 Figure 3.5e Optimum Mass Points Distribution o f ISAP/OSC Constraints

W ith A = 6 .0 , S C =10.0, M =

6

Figu re 3.8a Output P D F o f IS A P / O S C Constraints

W ith A = 1 .0 , SC =5.0, M = 3 , and S N R = -3 .0 1 d B 65

Figu re 3.8b Output P D F o f IS A P / O S C Constraints

W ith A = 1 .5 , SC =6.0, M = 3 , and S N R = 0 .5 1 2 d B 65

Figure 3.8c Output P D F o f IS A P / O S C Constraints

W ith A = 2 .0 , SC =6.0, M = 3 , and S N R = 3 .0 1 d B 65

Figu re 3.8d Output P D F o f IS A P / O S C Constraints

W ith A = 2 .5 , S C =7 .0, M = 4 , and S N R = 4 .9 4 9 d B 65

Figure 3.8e Output P D F o f IS A P / O S C Constraints

W ith A = 3 .0 , SC =7.0, M = 4 , and S N R = 6 .5 3 2 d B

66

Figure 3.8f Output P D F o f IS A P / O S C Constraints

W ith A = 4 .0 , SC =8.0, M = 5 , and S N R = 9 .0 3 1 d B

66

Figu re 3.8g Output P D F o f IS A P / O S C Constraints

W ith A = 5 .0 , SC =9.0, M =

6

66

Figure 3.8h Output P D F o f IS A P / O S C Constraints

W ith A = 6 .0 , SC =10.0, M =

6

66

Figu re 4.1 B lo c k D iagra m o f T -user M u ltip le A ccess Com munication

System 69

Figu re 4.2 N oiseless T -user B inary A d d e r M A C M o d e l 72

Figure 4.3 N oiseless T -user M -a ry A d d er M A C M o d e l 72

Figure 4.4 N u m ber o f O/P Signal L e v e ls versus I/P Signal L e v els

F o r T-u ser M -ary A d d e r M A C 73

Figure 3.7h Output PD F o f ISA/OSC Constraints

76 Figure 4.5 N o is y T -user M -a ry A d d er M A C M o d e l

Figure 4.6 Equivalent N o is y T-user M -a ry A d d e r M A C M o d e l 77

Figure 4.7a N oiseless T -u ser M -ary A d d e r M A C Output Probability

Distribution ( T = l , M =2, L = 2 ) 78

Figure 4.7b N oiseless T -u s e r M -ary A d d e r M A C Output Probability

Distribution (T = 2 , M = 2 , L = 3 ) 78

Figure 4.7c N oiseless T -u ser M -ary A d d e r M A C Output Probability

Distribution (T = 3 , M = 2 , L = 4 ) 78

Figure 4.7d N oiseless T -u ser M -ary A d d e r M A C Output Probability

Distribution (T = 4 , M =2, L = 5 ) 78

Figu re 4.8a N o is y T-u ser M -a ry A d d er M A C Output Probability

D ensity Function (T = 2 , M = 2 , L = 3 , S N R = 2 0 d B ) 79

Figure 4.8b N o is y T-u ser M -a ry A d d er M A C Output Probability

D ensity Function (T = 2 , M = 2 , L = 3 , S N R = 1 0 d B ) 79

Figure 4.8c N o is y T-u ser M -ary A d d er M A C Output Probability

D ensity Function (T = 2 , M = 2 , L = 3 , S N R = -1 0 d B ) 79

Figure 4.8d N o is y T-u ser M -ary A d d er M A C Output Probability

D ensity Function (T = 2 , M = 2 , L = 3 , S N R = -2 0 d B ) 79

Figure 4.9 T-user M -ary Frequency M A C W ith ou t Intensity Inform ation 82

Figure 4.10 Num ber o f O/P Signal L e v e ls versus I/P Signal L e v els

For T-user M -a ry Frequency M A C W ithou t Intensity Information 83

Figure 4.11 T-user M -ary Frequency M A C W ith Intensity Inform ation 85

Figure 4.12 Num ber o f O/P Signal L e v e ls versus I/P Signal L e v els

For T-user M -a ry Frequency M A C W ith Intensity Inform ation

86

Distribution 94

Figu re 4.14 C apacity o f T -u ser M -ary A d d e r M A C W ith Actual O/P

Distribution 94

Figu re 4.15 C apacity o f T -u ser M -a ry A d d e r M A C versus E/No (d B )

(M = 2 , A n tipodal S ign a llin g S ch em e) 95

Figure 4.16 C apacity o f T -u ser M -ary A d d e r M A C versus E/No (d B )

(M = 2 , O n -O ff K e y in g S ch em e) 95

Figu re 4.17 C apacity o f T -u ser M -ary A d d e r M A C versus E/No (d B )

(M = 2 , B inary S ign a llin g S ch em e) %

Figure 4.18 C apacity o f T -u ser M -a ry A d d e r M A C versus E/No (d B )

(M = 4 ) 96

Figure 4.19 Capacity o f T -u ser M -a ry A d d e r M A C versus E/No (d B )

(M =

6

Figure 4.20 C apacity o f T-u ser M -a ry A d d e r M A C versus E/No (d B )

(M =

8

Figure 4.21 C apacity o f T -u ser M -ary F requ en cy M A C W ithou t Intensity

Inform ation (w ith U n ifo rm O/P Distribution) 100

Figure 4.22 C apacity o f T-u ser M -a ry F requ en cy M A C W ithout Intensity

Inform ation (w ith A ctu a l O/P D istribution) 100

Figure 4.23 C apacity o f T -u ser M -a ry F requ en cy M A C W ith Intensity

Inform ation (w ith U n ifo rm O/P Distribution) 101

Figure 4.24 Capacity o f T -user M -a ry F requ en cy M A C W ith Intensity

Inform ation (w ith A ctu a l O/P Distribution) 101 Figure 4.13 Capacity o f T-user M-ary Adder M A C With Uniform O/P

(w ith midpoint D ecision T h resh old s) 122

Figure 5.2 T-user C C M A Channel O/P S E R

(w ith Optimum D ecisio n Th resh olds) 122

Figure 5.3 H D . C C M A D ecoder C E R 129

Figure 5.4 M L S D _ C C M A D ecoder C E R 129

Figure 5.5 C C M A D ecod in g Sch em es C E R (C o d e 1) 130

Figure 5.6 C C M A D ecod in g Sch em es C E R (C o d e 2 ) 130

Figure 5.7 C C M A D ecoding Schem es C E R (C o d e 3 ) 131

Figure 5.8 C C M A D ecoding Sch em es C E R (C o d e 4 ) 131

Figure 5.9 C C M A D ecoding Sch em es C E R (C o d e 5 ) 132

Figure 5.10 C C M A D ecod in g Sch em es U sers Sin k S E R (C o d e 1) 133

Figure 5.11 C C M A D ecod in g Sch em es U sers Sin k S E R (C o d e 2 ) 133

Figure 5.12 C C M A D ecod in g Sch em es U sers S in k S E R (C o d e 3 ) 134

Figure 5.13 C C M A D ecoding Sch em es U sers S in k S E R (C od e 4 ) 134

Figure 5.14 C C M A D ecod in g Sch em es U sers S in k S E R (C o d e 5 ) 135

Figu re 6.1 B lock Diagram o f M F S K _ C C M A Transmission System 141

Figu re 6.2 B lock Diagram o f S q u are-La w D em odulator 144

Figu re 6.3 B lock Diagram o f Z erocrossin g C ou n tin g D em odulator 148

Figure 6.4 B lock Diagram o f Quadrature D em odulator 152

Figure 6.5 System 1 Demodulator Input and Output W a veform s 160

Figure

6.6

Figure 6.7 Demodulator S E R versus E/No (d B ) 163

Figure

6.8

T a b le 4.2 C om posite S ign a l Sym bols F or A n tip o d a l Sign a llin g (T = M = 2 ) 92

T a b le 4.3 Com posite S ign a l Sym bols F o r O n - O ff K e y in g (T = M = 2 ) 93

T a b le 5.1 2-user U n iqu ely D ecodable C o d e 105

T a b le 5.2 Forbidden and Nearest A d m issib le C o d e w o rd s F or 2-user C ode 1 114

T a b le 5.3 D ecod in g D ecisio n T able fo r 2-user C o d e 1 116

T a b le 6.1 2-user S q uare-Law Demodulator O utput 146

T a b le 6.2 Norm alised Z C Counts w ith D iffe r e n c e Procedure 149

T a b le 6.3 Norm alised Z C Counts w ith Sum P ro ced u re 149

T a b le 6.4 2-user 2 F S K Z C Demodulator Output 151

T a b le 6.5 2-user 2 F S K W ith Intensity In form a tion Quadrature

Demodulator Output 155

T a b le

6.6

Dem odulator Output 156

T a b le 6.7 2-user 2 F S K W ithou t Intensity In fo rm a tio n Quadrature

Demodulator Output 156

T a b le

6.8

Demodulator Output 157

Table 4.1 Composite Signal Symbols For Binary Signalling (T=M =2) 91

Acknowledgments

I w o u ld lik e to express m y sincere gratitude to m y su pervisor, Dr. B. H onary, for

his keen guidance, encouragement, and valu able com m en ts throughout this w ork. I

w ould also lik e to thank Pro fessor M . D arnell fo r his v a lu a b le comments during the

course o f this research. Thanks are due t o D r. G . M arka rian fo r his ad vice and

assistance in th e w ork o f Chapter fiv e.

A ls o I w o u ld like to thank m y colleagu es in the H u ll-W a rw ick Communication

Research G rou p , fo r their encouragements, h elp fu l com m en ts and friendship. I am also

indebted to m y cousin Issam A m in and all m y frien ds w ith ou t whose friendship,

encouragements and support I w ou ld not ha ve been able t o com p lete this work.

F in ally, I w o u ld lik e to take this opportunity to thank m y parents and every

m ember o f m y fa m ily fo r th eir support, care and continual encouragem ents through out

this work.

Declarations

T h e fo llo w in g is a list o f the materials w h ich h a ve e ith e r been published o r

submitted fo r publication , during the course o f this research program , along w ith the

sections to w h ich th ey relate. Th ese materials are the direct results o f the w o rk carried

ou t b y th e author.

- "Inform ation C a p a city o f A d d itive W h ite Gaussian N o is e Channel w ith Practical

Constraints", IE E Proceedin gs, V o l. 137, P t I, N o . 5, pp295-301, O c t 1990.

(R eleva n t to Chapter 3)

- "C a p a city o f T -u s e r C ollaborative C od in g M u ltip le A ccess S ch em e Operating o v e r A

N o is y Chan nel", IE E Electronics Letters, V o l. 25, N o . 11, pp742-744, M a y 1989.

(R elevan t to Chapter 4 )

- "C olla b o ra tive C o d in g M ultiple A ccess Channel", C o llo q u iu m o n Radio C om m unica­

tio n Tech niqu es and Systems, U niversity o f W a rw ick , July 1989.

(R elevan t to Chapter 4 &

6

- "Perfo rm an ce S tu d y o f C ollaborative C od in g M u ltip le A c c e s s O v e r N o is y Channel",

P ro ceed in gs o f Fourth Joint Sw edish-S oviet International W o rk s h o p on Information

T h e o ry , p p l57 -1 6 4 , A u g.2 7-S ept.l 1989.

(R elevan t to Chapter 4 &

6

- "Inform ation Transm ission Capacity and Error C ontrol C a p a b ility o f Collaborative

C oding M u ltip le A ccess S ystem ", Proceedings o f Secon d B a n g o r Symposium on

Com munications, p p 195-198, 23-24 M a y 1990.

(R eleva n t to Chapter 4 & 5)

- "S o ft D ecisio n D ecod in g Technique fo r C o llab orative C o d in g M ultiple Access

Channels", Proceedin gs o f T h ird IE E C onferen ce o n T eleco m m u n ication , Edinburgh,

ppl41-147, 17-20 M arch 1991.

(R e lev a n t to Chapter 5)

- " L o w C o m p le x ity S o ft D ecisio n Decoding Tech n iqu e fo r T-u ser C olla b o ra tive C oding

M u ltip le-A ccess Channels", IE E Electronics Letters, V o l. 27, N o . 13, p p l 167-1169,

June 1991.

(R e lev a n t to Chapter 5)

- "C olla b o ra tive C od in g M u ltip le Access E m p lo yin g M anch ester and C M I Codes",

Proceedings o f Fourth B a n gor Symposium on Com munications, 2 7 -2 8 M ay 1992.

(R eleva n t to Chapter 5 )

- "C o lla b o ra tive C od in g and Decoding Tech niqu es fo r M u ltip le A ccess Channels",

Submitted fo r Publication to IE E Proceedings, P t I, M a y 1992.

(R e lev a n t to Chapter 5 )

Abstract

T h is thesis investigates collabo rative cod in g multiple access (C C M A ) channel com munication schemes. T h e C C M A schemes potentially perm it e ffic ie n t simultaneous transmission b y several users sharing a com m on channel, without su bdivision in tim e, frequency o r orth ogonal codes. T h e main areas o f investigation in clu d e the information transmission capacity fo r sin g le and multiple access channels, coding/decoding techniques and practical system design fo r C C M A schemes.

T h e inform ation transmission capacity o f a sampled and quantised single access A W G N channel is developed. It is determined and optim ised w h en th e channel input and output are lim ited by certain practical constraints. Th ese investigation s have led to the d evelo pm en t and determ ination o f the inform ation transmission ca p a city o f multiple access channels. T h e capacity o f a multiple access channel is studied fo r tw o different classes o f T -u ser channel m od els fro m both theoretical and practical points o f view . It is shown, in prin ciple, that high er transmission rates or, eq u iva len tly, m ore reliable com munication than w ith tim e sharing is achievable em p lo yin g th e same signalling

alphabet

T h e C C M A schemes, in addition to p ro vidin g the m ultiple access function, can also in corporate a certain d egree o f error control capability. T w o main decoding techniques, hard decision and maxim um likelih ood so ft decision, a re presented w ith uniquely d eco d a b le C C M A schemes. A n ew lo w com p lex ity m axim u m likelihood decoding techn ique is described and analysed. R elia b ility p erform an ce o f various collaborative c o d e s is studied b y simulation e m p lo yin g these d e co d in g techniques. It is shown that u n iqu ely decodable schemes perm it the multiple a ccess function to be com bined w ith forw a rd error correction. It is also foun d that soft d e cis io n decoding can provide an e n e rgy gain o v e r hard decision decoding.

T h e fin a l area o f investigation is a practical C C M A m odem system design to combine c o lla b o ra tive codin g and modulation. A n M -a ry frequ en cy sh ift keyin g based m odulation sch em e is described fo r the T-user C C M A schemes. T h r e e particular types o f dem odulation techniques, square-law, zerocrossing counting, and quadrature receiver, are described. T h e s e techniques are developed in softw are, tested an d evaluated o ver

noiseless and n o isy channels.

Chapter . !

Introduction

T h e purpose o f m o d em com m unication th eory is to enable the d e sig n o f systems

w h ich facilitate rapid, relia ble, and e ffic ie n t transfer o f inform ation th rou gh a medium

w h ich is called a com m u nication channel. A telephone w ire transm ission line, o r radio

frequ en cy electrom agn etic propagation system are tw o v e ry co m m o n exam ples o f

com munication channels. Intuitively, a com munication channel is an y m edium w hich

supports the propagation o f energy fro m a source to a destination with s u fficien t control

to a llo w m ovem en t o f som e data.

T h e classical m o d e l o f a com munication system has a sin gle transm itter sending

inform ation to a rec e iv e r through a channel w h ich in som e w a y corrupts the transmitted

information. T h is is a sin g le access com m unication channel (S A C ). D evelo pm en ts in

satellite com m u nication systems, com puter com munication n etw orks, m obile radio

systems, and other com m unication system s in v o lvin g multi-user ha ve le d communica­

tio n systems designers to investigate the simultaneous transmission o f inform ation fro m

several terminals o v e r a com m on com m unication channel. A n important m o d el o f multi­

user com munication is the m ultiple access com munication channel (M A C ) .

T h e inform ation th eo ry o f S A C [Shannon 1948] has shown that, noise and other

disturbances on the channel d o not lim it the relia bility by w h ich d ig it a l data can b e

transmitted but rather o n ly lim its the rate at w h ich data o f arbitrarily h ig h reliability can

be transmitted. T h e highest rate at w h ich such relia ble data can be transmitted o v e r a

channel is know n as the capacity o f the channel. T h e inform ation theory o f M A C has

shown that, multiple users can communicate data w ith arbitrarily small p ro b a b ility o f

error o v e r a com mon channel provided that the rates o f the individual data streams lie

w ith in the capacity region fo r the channel. T h e set o f rates at w h ich simultaneous

relia ble transmission is possible is called the capacity region o f M A C . Shannons

capacity theorem g ives us a theoretical value fo r the error fre e capacity o f a channel,

g ive n that the time taken to evaluate the data is infinite. H o w ever, in m ost practical

circumstances, this is o f little use as any practical demodulation/decoding s ch em e must

g iv e a result in a finite period o f tim e. Th erefo re, the practical system d e sig n e r must

keep in m in d the theoretical channel capacity, and probably m ore im portantly, certain

practical restrictions w hich must also be satisfied.

O n e o f the basic w a ys o f increasing the throughput o f a com m unications resource

is to m ake the allocation o f the communications resource m ore efficien t. T h is approach

is the dom ain o f multiple access communications. T h e problem is to e ffic ie n t ly allocate

portions o f the fixed communications resource to a large number o f users w h o seek to

com m u nicate digital in form ation to each other. T h ere are many w ays o f distributing the

com munications resource am on g the active users. H ow ever, the purposes h e re are to

rule out conventional channel sharing techniques such as T D M A , F D M A an d C D M A .

M o re in tu itively, the rationale behind this is to investigate collaborative c o d in g multiple

access ( C C M A ) techniques b y which a sin gle transmission medium can b e shared

e ffic ie n tly and in a distributed fashion am ong m any users.

C ollaborative codin g constructions have foun d short codes w h ich a re easy to

d eco d e such that, the a ctive users which transmit independently (i.e., w ith o u t prior

reservations and without feedback during transmission) through the same chan nel can

be d eco d ed u n iquely at the receiver. In particular, there exist collaborative c o d e s w h ich

a llo w t w o o r m ore users to share the same transmission bandwidth and a b le to

com m unicate at a com bined inform ation rate w h ich is greater than unity. T h a t is, the

summary rate o f the users is greater than the ideal rate (unity) w h ich can b e a c h ieved

by m eans o f tim e sharing o r T D M A . Sin ce th e transmission channel is alw a ys

susceptible t o external noise, a co llab o rative co d in g design needs, not o n ly to be

un iquely d eco dable but also must b e able to correct transmission errors.

In practical systems, the transfer o f co llab o rative coded messages in v o lv e s the

utilisation o f various m odules, i.e. m odulator, demodulator and the com m u nication

m edium. T h e modulator, w h ich is em p lo yed at the transmitter side, translates th e coded

m essage stream into a suitable form a t fo r transmission o v e r the m ultiple access

com m u nication medium. O n the other hand, the demodulator, is situated at the r e c e iv e r

and p erform s the reverse operation to that o f the modulator. T h e dem odu lation process

in v o lve s the detection o f th e received com posite sign al and the subsequent m a p p in g o f

these signals into the form at o f the o rigin al m essage stream.

Investigations o f inform ation transmission capacity o f both S A C and M A C ,

coding/decoding, and practical system design f o r theses C C M A schemes are o f

con siderable im portance to p ro vid e the overa ll e ffic ie n t m ultiple access system . T h e

w o rk o f this thesis is a contribution towards these objectives.

T h e seco n d Chapter o f this thesis review s the principles and various techniques

o f m u ltiple access com munications. A perspective, classification and discu ssio n o f

m ultiple access com munications are g iven . F o llo w in g this, the m ost com m on techn iques

o f M A C are discussed. A description o f C C M A schemes is also presented in th e same

section. T h e M A C m odels describing the form o f a signals interaction o v e r a channel

are presented w ith som e examples. T h e m ain achievem ents o f the inform ation theory

and coding/decoding approaches to the M A C are also b rie fly rev ie w e d and discussed

in this Chapter.

In C h apter three, the inform ation transmission capacity o f a sam pled and

digitised sin g le access A W G N channel lim ited b y input and output practical constraints

is described. T h e channel input is characterised b y th e input signal am plitude and

average pow er, and th e channel output is characterised b y the output signal c lip p in g due

to quantisation ap p lied at the receiver. T h e input signal amplitude/output sign al clip pin g

(IS A / O S C ) constrained capacity, and the input signal am plitude and average

power/output sign al clippin g (IS A P / O S C ) constrained capacity are determ ined and

optim ised separately. T h e optim um input signal am plitude distributions and the optim um

output signal c lip p in g that m axim ises the capacity are also determined. T h e s e tw o

capacities are d eve lo p e d b y softw a re and simulation results and discussions are

presented at the en d o f this Chapter. T h e w o rk described in Chapter three g a v e insight

and m ore understanding to the m ore com plica ted case o f M A C capacity w h ich is the

subject o f in vestigation in Chapter four.

Chapter fo u r is concerned w ith theoretical investigations o f the inform ation

transmission ca p acity o f M A C s . T w o particular types o f T-user M -a ry M A C models,

interesting fro m their theoretical and practical applications, are introdu ced and

described. T h e T -u ser M -a ry frequ en cy M A C is presented in tw o form s, w ith and

without inten sity inform ation o f the rec e iv e d signal en ergy level. T h e inform ation

transmission ca p acity is d evelo ped , th eoretically, in bits per channel use, f o r these

m odels in noiseless and noisy channel conditions. T h is capacity is sim ulated in softw are

fo r various transmission systems e m p lo yin g coherent and noncoherent com b in in g o f

signals at the channel and fo r various number o f users, T , and input signal levels. M .

T h e practical im plications o f the M A C capacity is also discussed.

Chapter f iv e investigates the capability o f C C M A schemes to p ro vide the

m ultiple access function as w e ll as the channel error control. U n iqu ely decodable c o d in g

schemes are g iven to p ro vid e these functions. Hard decision C C M A (H D _ C C M A ) and

maxim um likelihood soft decision C C M A (M L S D _ C C M A ) d eco d in g techniques are

presented. These techniques are described together with sym bol-by-sym bol H D

(S B S _ H D ) decoding. A n e w lo w c om p lex ity maxim um likelih oo d d eco d in g technique

is presented to utilise the error control capability. T h e decoding procedure and algorithm

fo r this technique are g ive n . A particular 2-user uniquely decodable schem e is analysed

w ith this new technique. T h e error probability is derived for the T -u ser binary channel

m odel em p lo yin g H D _ C C M A and M L S D _ C C M A decoding techniques. T h e th eoretical

calculations are presented fo r a particular 2-user uniquely decodable case. F in ally this

Chapter ends w ith sim u lation o f various 2-user uniquely d eco dable schemes. T h e

relia bility perform ance o f these codes em p lo yin g H D _ C C M A and M L S D _ C C M A is

evaluated in the p resence o f A W G N conditions. T h e results are presented in the fo rm

o f sym bol and c o d ew o rd error rates as a function o f signal to noise ratios.

Practical d esign o f C C M A m odem is investigated in Chapter six. T h e design o f

C C M A modulation schem e based on the M -ary frequency sh ift k eyin g (M F S K )

modulation scheme is described. T h ree particular types o f dem odulation techniques are

investigated w ith com b in ed collaborative coding and m odulation signals. T h e s e

techniques are square-law , zerocrossing counting, and quadrature demodulators. T h e

quadrature dem odulator is presented and described fo r tw o m odels, w ith and w ith out

intensity information. T h e o verall designed C C M A systems are d evelo p ed in softw a re,

and v e rifie d in a noiseless channel. A n assessment and com parison o f the relative

relia b ility perform ance o f these schemes is carried out b y simulation o v e r A W G N

channel. T h e relative merits o f the schemes are discussed, particularly w ith respect to

their im plem entation com p lex ity.

T h e thesis ends w ith a conclusions and further future w orks on each Chapter o f

this thesis.

This page has been intentionally left blank

Chapter 2

Introduction to Multiple Access Communications

2.1 Introduction

In this chapter, w e b rie fly review the prin ciples and techniques o f multiple access

com munications. Sin ce a general introductions to the multiple access communications

channel h a ve been g iv e n in details elsew here e.g. [M eulen 1977, M eulen 1986, El

G am al and C o v e r 1980, Farrell 1981, W o l f 1981, and Gallager 1985], the reader is

referred to these w o rk s f o r m ore thorough treatment o f the introductory material. W e

shall poin t out these w o rks w h en ever is required throughout this chapter.

2.2 M u l t i p l e A c c e s s C h a n n e l

C om petition fo r the use o f existin g communications resource leads to the

question o f simultaneous channel usage b y m ore than on e user. T h is kind o f

com m u nication situation is known as M A C and illustrated in F igure 2.1, in which there

are several users com m u nicating w ith on e r ec e iv e r o ver a com m on channel. Examples

o f m ultiple access communications include several mini-computers sending data

simultaneously to a large computer [A bram so n 1970, and Sch w artz 1977], several

ground stations accessin g a satellite repeater [S tig litz 1973, Ince 1978, Nirenberg and

Rubin 1978, and S o m m er 1968], several m o b ile radio to base station [Steele 1988,

Farrell 1985, and Farrell, e t al., 1986], etc. o r sim ply several students questioning a

p rofessor at th e sam e tim e.

In the M A C com m u nication situation, each transmitter is fe d b y an in form ation

source, and each in fo rm atio n source generates a sequence o f messages. T h e generated

successive m essages arrive at random instants o f tim e to be transmitted. T h e received

signal is corrupted b y noise and mutual interference betw een the transmitters during

transmission o v e r the channel. Th erefo re, the m ain issues in m ultiple access

com m unication system s are interference betw een users, noise, and the random, ex'

"bursty", arrivals o f m essages. C lassification o f the m ain research w o rk o n multiple

access com m u nication accordin g to G allager [G a lla ger 1985] is shown in F igu re 2.2.

Multiple Access Communication

Info rm a tion T h e o ry C o llisio n R e so lu tio n Sp rea d Spe ctrum

Figure 2.2

Classification of Multiple A c c e s s Communication

T h is classification show s that there ha ve been m ain ly three bodies o f research on

m ultiple access com m u nications, each using to tally differen t models. Th ese main areas

are m u ltiple access inform ation theory, co llis io n resolution and spread spectrum.

T h e m ultiple access in fo rm atio n theoretic approach w as initiated in 1961 by

Shannon in his fundam ental paper [Shannon 1961], and established in 1971 w ith a

cod in g th eorem d eve lo p e d b y [A h lsw ed e 1971, and L ia o 1972]. T h is approach

appropriately m od els the n o ise and interference o f th e M A C but ignores the random

arrival o f m essages. It is ta citly assumed b y inform ation theoretics that the sources ha ve

a reservo ir o f data to send w h ich is n ever em pty. Thu s the theoretical results in this area

do not address the question o f the delay that arises in m ultiple access systems because

o f the random arrival tim es o f data to be transmitted. T h is assumption is adequate fro m

the th eoretical poin t o f v ie w , since the random arrivals o f messages can b e sm oothed

out b y appropriate source c o d in g [G a lla ger 1985]. F ro m a m ore practical point o f v ie w

this m o d el is not adequate because the lon g tim e intervals required fo r the source

arrivals to be sm oothed ou t are ty p ica lly fa r greater than the tolerable delays. F or m ore

inform ation refe r t o [M eu len 1977, M eu len 1986, W y n e r 1974, and E l G am al and

C o v e r 1980].

T h e c o llis io n resolution approach [M assey 1985, M assey and M ath ys 1985,

Abram son 1985, and M assey 1986], has alw a ys concentrated on the random arrival o f

m essages and on the transm ission delays w h ich are due to the interference betw een

users, but has gen era lly ign o red all other aspects o f the underlying com munication

process (e.g. n o ise). T h is approach to the m ultiple access com munication came in 1970

w ith A b ram so n ’ s A L O H A n etw ork [A bram son 1970]. T h e basic idea o f this system w as

that w h en ever a m essage (o r packet) arrived at a transmitter, it w ou ld sim p ly be

transmitted, ignoring all other transmitters in the network. I f another transmitter was

transmitting in an overlappin g interval, interference w ou ld prevent the message from

being correctly received, n o acknow ledgm en t w ould be sent, and the transmitter would

try again later. T h e later tim e w ou ld b e pseudorandomly chosen to a v o id the certainty

o f another collision i f both transmitters w aited the same tim e. O v e r the years, this basic

strategy has been im proved, generalised, and analysed in many w ays. For a more

detailed exposition o f the co llision resolution approach refer to the special issue on

random access w h ich consist o f m any papers [M assey 1985, M assey and Mathys 1985,

Abram son 1985, and M assey 1986].

Spread spectrum [C o o k , et al., 1982, Sch oltz 1982, and Pickh oltz, et al., 1982],

is a m ode o f com munication o rig in a lly developed to protect against ja m m in g in a

m ilitary environm ent. F or multiple access communication using spread spectrum several

sources can transmit at on ce using d ifferen t modulatin g sequences, and each w ill look

lik e broadband noise to the others. Th erefo re, in the multiple access spread spectrum

approach the interference fro m other users is treated as additional, poten tially intelligent,

noise. F o r m ore detailed discussions and w ork carried in this area refe r to the special

issue on spread spectrum w hich con sist o f many papers [C ook , e t al., 1982, Scholtz

1982, and Pickh oltz, et al., 1982].

2.3 Multiple Access Techniques

In m ulti user systems, there are many w ays o f sharing the communications

resource am ong the a ctive users [S k la r 1988 pp476-531]. T h e m ain objective o f all

these m ultiple access techniques is that various signals share a communications resource

without creating unmanageable interference to each other in the detection process. The

allo w able lim it o f such interference is that signals on on e com munications resource

channel should not sign ifica ntly increase the probability o f error in another channel.

Classification o f the m ost com m on m ultiple access techniques togeth er w ith the C C M A

under investigation is g ive n in Figu re 2.3.

Multiple Access Methods

/

Freq u ency D iv isio n Tim e D iv isio n C o d e D iv isio n C olla b o rative C o d in g M ultiple A c c e s s M ultiple A c c e s s M ultiple A c c e s s M ultiple A c c e s s

Figure 2.3

Classification of Multiple A c c e s s M ethods

A b rief description o f these techniques is g ive n here.

2.3.1 F re q u e n c y D ivisio n M u ltip le A ccess ( F D M A )

In this technique [Sklar 1988 pp476-491], th e com munications resource sharing

is accom plish ed by allocating certain frequ en cy bands as shown in Figu re 2.4, in which

each user is assigned o n e o f these bands to com municate. T h e assignment o f a user to

a frequ en cy band is lo n g term o r permanent, the com munications resource can

simultaneously contain several spectrally separate signals. In its sim plest form , each

subscriber operates w ith in a separate operating frequ en cy band. M utual interference

between subscribers is kept to a m inim um b y using nonoverlapping frequ en cy bands.

F or exam ple, the first frequ en cy band contains signals that operate betw een frequencies,

f 0 and f „ the seco n d betw een frequ en cies f 2 and f 3, and so on. T h e spectral regions

between assignments, called guard bands, act as b u ffer zones to reduce interference

between adjacent frequ en cy channels.

F re q u e n cy

Figure 2.4

Frequency D ivision Multiple A c c e s s

T h e F D M A channels require n o synchronisation o r central tim ing, in w h ich each

channel is a lm ost independent o f a ll oth er channels. T h e main advantages o f F D M A is

its sim p licity an d the lo w cost o f the equipm ent required. H o w ever, on e o f th e problem s

w ith F D M A is the cross talk b etw een different channels that can result in some

perform ance degradation [N iren b erg and Rubin 1978, and Sklar 1988 pp476-491].

?,?.2 Time Division Multiple Agyess (T P M A )

M u ltip le access b y tim e d iv is io n [Sklar 1988 pp476-491] is accom plish ed by

assigning ea ch o f the users the fu ll spectral occu pan cy o f the system f o r a short

duration c a lle d a tim e slot, selected to elim in ate signal overlap at the intended

receiver(s) as show n in Figure 2.5. T h e unused tim e region s between slot assignments,

called the guard tim e, a llo w fo r so m e tim e uncertainty between signals in adjacent time

slots, and thus a ct as bu ffer zones to reduce interference.

Tim* »lot 1 T l«« Slot 3

Figure 2.5

Time Division Multiple A c c e s s

In T D M A , tim e is segm ented in to intervals ca lle d frames. Each frame is further

partitioned in to assignable user tim e slots. T h e fra m e structure repeats, so that a fix ed

T D M A assignm ent constitutes on e o r m ore slots that p e rio dically appear during each

fram e tim e. E ach station transmits its data in bursts, tim ed so as to arrive coincident

w ith its designated tim e slot(s). W h en the bursts are received , they are retransmitted

together w ith the bursts fro m other stations. A rec e iv in g station detects and

dem ultiplexes the appropriate bursts and feeds the in fo rm atio n to the intended user.

T D M A has found w id e application because o f its ability to perm it many

subscribers to access a com m on channel without causing mutual interference. T D M A

systems m ay s u ffer fro m other problem s. Predom inant am on g these are. strict inter-user

synchronisation o r the extra channel tim e required t o ensure the T D M A channel

allocations, e x cess hardware required to participate in a structured T D M A netw ork, and

the delay in accessin g the channel [D ill 1977, Rubin 1979, N irenberg and Rubin 1978,

S tiglitz 1973, and Sklar 1988 pp476-491].

2.3.3 Code Division M ultiple Access (C D M A )

Figure 2.6, illustrates the communications resource bein g partitioned by the use

o f a hybrid com bination o f F D M A and T D M A k n o w n as C D M A .

Fre q u e n cy

Sig na l 3 : Sig nal 1 Signal 3

Sig na l 2 Signal 3 Sig na l 2

Sig na l 1 I Sig nal 2 Sig na l 1

* SM i s T im e

Figure 2.6

C o d e Division Multiple A c c e s s

C D M A is an application o f spread spectrum techniques [C o o k , et al., Scholtz

1982, Pickh oltz, et al., 1982, and Sklar 1988 pp491-493]. A spread spectrum

com m unication system can be defin ed as on e in w h ich : (a ) th e transmitted signal

bandwidth is m uch g reater than the m inim um bandwidth necessary to send the message

inform ation, (b ) all users have access to the w h o le tim e frequ en cy space o f the channel,

(c ) som e function other than the m essage is used to determ ine th e bandwidth o f the

transmitted signal, and (d ) the signals, codes, o f each user are all mutually orthogonal

in som e sense s o that the signals, codes, m ay b e unscrambled at the receiver by

correlation [In ce 1978].

Spread-spectrum techniques can be classified into tw o m a jo r categories: direct-

sequence and frequ en cy hopping. In direct-sequence schemes, the data signal is

modulated on to a d igita l, pseudo-random code sequence w h ich has a d igit rate much

higher than that o f the data. Each o f the user groups is g ive n its o w n cod e. T h e user

codes are approxim ately orth ogonal, s o that the cross-correlation o f t w o differen t codes

is nearly zero. T h e signals to b e transmitted are m odulated b y these nearly orthogonal

sequences o v e r much broader frequ en cy band than necessary. B y using appropriate

sequences, each transmitted signal w ill look like broadband noise to the others. T h e

rec e iv e r can use the same sequence to despread the received sign al to reco ver the

transmitted messages. Frequ en cy hoppin g schemes, can be easily v ie w e d as the short­

term assignment o f a frequ en cy band to various sign al sources. T h e data signal is

modulated on to a sinusoidal carrier, the frequ en cy o f w h ich is caused to change in

discrete increments, accordin g to a pattern determ ined b y a pseudo-random code

sequence. Each user is g ive n a set o f hoppin g patterns such that each pattern o f a g iven

set is nearly orthogonal to all patterns o f other sets.

T h e most important advantage o f C D M A schemes, com pared to T D M A , is that

all the participants can share the fu ll spectrum o f the resource asynchronously. There

is no need to precise tim e coordination am ong the various sim ultaneous transmitters,

i.e., the transmission tim es o f the d ifferen t users’ sym bols d o not ha ve to coincide. T h e

orth ogonality between user transmissions on d ifferen t codes is not affected by

transmission tim e variations. T h is w ill becom e clea r upon clo ser exam ination o f the

auto-correlation and cross-correlation properties o f th e codes. T h e s e schemes are

advantageous under certain circumstances in that th ey perm it fle x ib ility as to the

number and a ctivity o f the users, they degrade g ra cefu lly as the number o f users

increases, and there is an automatic trade-off betw een the number o f users and the

degree o f error protection.

T h e T D M A , F D M A , and C D M A techniques m a y also be used in either fix e d or

demand assigned m ultiple access m odes. In the fix ed assigned m ultiple access m ode the

transmission form ats o f the techniques does not change, even though the traffic load

varies fro m tim e to tim e. In the demand assigned multiple access m ode, the formats o f

transmission o f the techniques are chan ged as needed, depending on the tra ffic demand.

C onsequently, the demand assigned m ode is more efficient, but it usually costs m ore

to im plem ent and maintain [Sklar 1988 pp476-497].

2.3.4 Collaborative Coding Multiple Access (CCMA)

In situations where the bandwidth is a very restricted resource, conservation o f

the spectrum, w h ich is a valuable and fin ite resource, is v e ry important. For example,

the radio frequ en cy bands represent an in flexib le resource and it is unlikely that

sign ifica n tly larger frequ en cy bands w ill becom e available. Th erefore, it is necessary

to investigate e ffic ie n t w ays o f sharing the available spectrum channels between as

m any users as possible. It is also o f considerable im portance to use a sim ple and

e ffe c tiv e m ultiple access cod in g technique capable o f error control as w e ll as the

m ultiple access function. T h e C C M A schemes permits potentially effic ie n t simultaneous

com m unications b y tw o o r m ore users in the same bandwidth without subdivision in

tim e, frequ en cy o r orthogonal cod e, though this scheme m ay be used in a m ixed format

w ith T D M A , F D M A , C D M A . It a llo w s a substantial increase in the number o f users

that can access the system simulateneously, leading to a higher com bined information

rate and hen ce a potentially m ore e ffic ie n t system. In addition to p ro vidin g the multiple

access function these schemes can incorporate certain degree o f error protection against

noise [F arrell 1981].

In co llab o rative codin g, digital m odulation and coding are intim ately related, and

the sim ultaneous signals fro m various users are demodulated together, as a combined

m u lti-level signal. T h is perm its the use o f r ela tiv ely short and sim ple codes in contrast

to the spread spectrum case. It can also be u sed w ith the single access m odulation

techniques (e.g. am plitude sh ift keyin g, phase sh ift k eyin g and frequency sh ift keyin g),

and applies to binary as w e ll as m ulti-level sign als, though at the cost o f an increase

in com p lex ity.

T h ese techniques ex ist w hich lie b etw een the tw o extrem e cases o f

TDMA

C D M A , and o ffe r in certain circumstances th e p o ssib ility o f rate sums high er than unity

w ith m odest synchronisation requirements [F a rrell 1981]. In

TDMA,

user synchronisation, o r poten tially wasteful tim e slot allocation is required. W h ere in

C D M A , simultaneous transmission without inter-user synchronisation can b e achieved,

but this can be wasteful o f bandwidth because o f the rela tively lo w number o f users that

can operate simultaneously.

C ollaborative co d e s exists fo r M A C and broadcast channel (B C ) [Farrell, et al.,

1986]. In the M A C case, each user is p ro vided w ith a code w hich enables the receiver

to d eco d e the individual in form ation streams, b y detecting the resulting com bined

signal. In the B C case, a com bin ed coded sign al is transmitted, and each rec e iv e r is able

to detect and decode th e inform ation destined f o r it. T h e B C is the inverse o f the M A C ;

the sources and their com m o n encoder are a ll at the same locations, wh ereas the

decoders and associated sinks are in d ifferen t locations. T h e inform ation broadcast may

be p riva te to each sink, o r m ay have com m o n elements.

T h ese techniques ha ve many applications, fo r exam ple, digital m o b ile radio

com m u nication systems [F arrell 1983, Farrell 1985, and Farrell, et al., 1986], in w hich

they can b e applied to both m obile-to-base and base-to-m obile transmission. These

techniques ha ve also been proposed fo r optical fib re communication system s [B rid ge

1986] and ty p es o f random access M A C , such as a satellite asynchronous m ultiple

access system [ W o l f 1978, and W e ld o n 1978].

2.4 Multiple Access Channel Models

T h e purpose o f M A C m od els is to describe h o w the input signals interact in the

channel to produ ce the channel output. M any M A C m od els h a ve been proposed and

used b y variou s researchers. C lassificatio n o f the discrete m em oryless M A C m odels

according to th e input c om bin in g function in the noiseless case, is shown in F igu re 2.7.

Discrete Input/Output

Multiple Access Channels

Real A d d e r O R X O R C h a n n e l C h a n n e l C h a n n e l

A N D S w itc h in g C olliaion C h a n n e l C h a n n e l C hann el

Figure 2.7

C lassification of Discrete Input M A C s

Each m od el is described v e ry b rie fly here.

(i) A d d er Channel: T h is is the m ost popular M A C m o d el and has been considered fo r

the in fo rm atio n th eo ry and c o d in g aspects by various authors [K asam i, et al., 1975,

Kasam i and L in 1976, Kasam i, et al., 1983, W e ld o n 1978, D eatt and W o lf 1978, C hang

and W e ld o n 1979, Ferguson 1982, Chang 1984, Braak and T ilb o r g 1985, Khachatrian

1982, Khachatrian 1984, and W ilso n 1988]. T h e channel output sym bol value is the

arithmetic sum o f the input sym bol values, in the absence o f noise. T h e T-user noiseless

adder M A C is d efin ed as a channel w ith T-input, and on e output g iv e n by;

w h ere X , is th e i-th channel input, Y is the channel output and the sign denotes real

addition. F or exam p le, consider the 2-user noiseless binary adder M A C shown in

Figu re 2.8.

0

1

-1 1 --- *--- 2

Figure 2.8

2 -u se r N o ise le ss B inary Adder M A C Model

It has tw o inputs, X , and X ^ i O . l }, and on e output Y , w h ich is the ordinary arithmetic

sum o f the inputs, Y = X , + X 2, Y e { 0 , l , 2 } . T h e arrowed lines represent the channel

conditional pro b ab ilities p ( Y | X ,,X 2). T h e adder channel is a lso know n as the binary

input erasure M A C [W o l f 1975], because the output sym b ol "1 " cannot be

unambiguously d eco d ed , ev en in the noiseless case.

(ii) O R Channel: This m od el is used b y various researchers in d iffe re n t communication

situations [S o m m er 1968, C oh en , e t a l„ 1971, V ite rb i 1978, G y o r fi and K erekes 1981,

and W o l f 1981]. T h e output o f th e channel can b e written f o r th e T -user noiseless

channel as;

X,

2

2

i

-1

w h ere the "V " sign is lo g ic a l O R and X|S{0 1 }. T h a t is, i f X f d en otes the binary input

o f the i-th user, then the output o f the channel is zero i f and o n ly i f X ,= X 2=...X T=0.

F or exam ple, the 2-user noiseless binary O R M A C is shown in F igu re 2.9, where the

channel output is "0 " i f X , = X 2= 0 and "1 " other w ise.

X,

X 2

Y

Figure 2.9

2 -u se r N o is e le s s B inary O R M AC Model

(iii) E xclu sive-O R (M o d u lo -2 ) Channel: T h is channel [W o lf 1975, and Farrell 1981),

output is m odulo-2 sum (e x c lu s iv e -O R fu n ction ) o f tw o cm- m ore input values. Thus all

inputs and the output ha ve th e same alphabet ( 0 , 1 ). This chan nel is also known as

m od u lo-2 addition channel. T h e T -u ser noiseless channel output can b e written as;

(2 .3)

where the sum m ation sign " 2 " is o v e r G F (2 ) and X , e { 0 , l } . For exam ple, the 2-user

noiseless binary ex c lu s iv e -O R M A C is show n in Figure 2.10, where the channel output

is the m odulo-2 sum o f tw o binary inputs.

X ,

X 2

Y

Figure 2.10

2 -u se r N o ise le ss Bin ary Exc lu sive -O R M AC Model

(iv ) A N D C hannel: T h is channel is also called binary m ultiplyin g channel as mentioned

in [M eu len 1977]. T h e capacity reg io n and cod in g strategy fo r this channel m od el is

considered b y [S ch alk w ijk 1982, and S ch alkw ijk 1983]. T h e noiseless T -u ser channel

output can be w ritten as;

K -n*,

,2-4>

i-i

where the m u ltip lyin g sign

"11"

binary m u ltiplyin g M A C is show n in F igure 2.11. T h e inputs and output are binary, and

the channel operation is defin ed by Y = X , X 2.

Xi

x

2

Y

0

1

0

0

0

1 1 1

Figure 2.11

2 -u se r N o ise le ss B in ary A N D M A C Model

( v ) S w itching C hannel: T h e sw itchin g channel m odel was o rig in a lly introduced because

it is in som e sense sim ilar t o the binary input real adder channel but exh ibits quite a

differen t behaviour in terms o f its cap acity region [V an ro ose and M eu len 1987, and

V an ro ose 1988]. For exam ple, the 2-user noiseless binary sw itchin g M A C is shown

in F igu re 2.12. T h e channel accepts t w o binary inputs and outputs a ternary sym bols

according to the b it w ise determ inistic transitions. Th erefo re, the channel output fo r the

2-user noiseless case can be written as;

w h ere the X,/0 is infin ity and X , e { 0 , l } . T h is is sim ilar to th e 2-user binary adder

channel w h ich has tw o binary input and ternary output.

(2.5)

0

1

1 1 --- >--- 1

Figure 2.12

2 -u se r N o ise le ss Binary Sw itching M AC Model

( v i) C ollision Channel: T h is channel m odel [G a lla g e r 1985, M assey 1985, M assey and

M ath ys 1985, and M assey 1986], is related t o the collision resolution approach

discussed in section 2.2. It is based on the assumption that w h en ever t w o o r m ore users

transmit simultaneously, the receiver can on ly detect that a c o llis io n took place. This

is can be w ritten as fo llo w s;

Y = X j; i f o n ly user i transmits

= C (c o llis io n ); i f tw o o r m ore users transmits (2.6)

2.5 Multiple Access Information Theory

T h e inform ation theory o f M A C is fundam entally con cerned w ith the simulta­

neous inform ation transmission o f several users through a com m o n channel, as

e ffe c tiv e ly as possible, in the presence o f arbitrary interference and noise. T h e main

ob jective o f this in form ation th eory is to characterise the capacity reg io n o f M A C fo r