Rao Channel Coding Techniques for Wireless Communications

2. Auflage 2019
ISBN: 978-981-15-0561-4
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 476 Seiten

Reihe: Forum for Interdisciplinary Mathematics

This book discusses the latest channel coding techniques, MIMO systems, and 5G channel coding evolution. It provides a comprehensive overview of channel coding, covering modern techniques such as turbo codes, low-density parity-check (LDPC) codes, space–time coding, polar codes, LT codes, and Raptor codes as well as the traditional codes such as cyclic codes, BCH, RS codes, and convolutional codes. It also explores MIMO communications, which is an effective method for high-speed or high-reliability wireless communications. It also examines the evolution of 5G channel coding techniques. Each of the 13 chapters features numerous illustrative examples for easy understanding of the coding techniques, and MATLAB-based programs are integrated in the text to enhance readers’ grasp of the underlying theories. Further, PC-based MATLAB m-files for illustrative examples are included for students and researchers involved in advanced and current concepts of coding theory.

Autoren/Hrsg.

Rao, K. Deergha

Inhaltsverzeichnis

1;Preface;7
2;Contents;9
3;About the Author;19
4;1 Introduction;20
4.1;1.1 Digital Communication System;20
4.2;1.2 Wireless Communication Channels;21
4.2.1;1.2.1 Binary Erasure Channel (BEC);21
4.2.2;1.2.2 Binary Symmetric Channel (BSC);22
4.2.3;1.2.3 Additive White Gaussian Noise Channel;22
4.2.4;1.2.4 Gilbert–Elliott Channel;23
4.2.5;1.2.5 Fading Channel;24
4.2.6;1.2.6 Fading;24
4.3;1.3 Statistical Models for Fading Channels;27
4.3.1;1.3.1 Probability Density Function of Rician Fading Channel;27
4.3.2;1.3.2 Probability Density Function of Rayleigh Fading Channel;28
4.3.3;1.3.3 Probability Density Function of Nakagami Fading Channel;28
4.4;1.4 Channel Capacity;29
4.4.1;1.4.1 Channel Capacity of Binary Erasure Channel;30
4.4.2;1.4.2 Channel Capacity of Binary Symmetric Channel;30
4.4.3;1.4.3 Capacity of AWGN Channel;30
4.4.4;1.4.4 Channel Capacity of Gilbert–Elliott Channels;32
4.4.5;1.4.5 Ergodic Capacity of Fading Channels;32
4.4.6;1.4.6 Outage Probability of a Fading Channel;34
4.4.7;1.4.7 Outage Capacity of Fading Channels;35
4.4.8;1.4.8 Capacity of Fading Channels with CSI at the Transmitter and Receiver;36
4.5;1.5 Channel Coding for Improving the Performance of Communication System;36
4.5.1;1.5.1 Shannon’s Noisy Channel Coding Theorem;36
4.5.2;1.5.2 Channel Coding Principle;37
4.5.3;1.5.3 Channel Coding Gain;37
4.6;1.6 Some Application Examples of Channel Coding;38
4.6.1;1.6.1 Error Correction Coding in GSM;38
4.6.2;1.6.2 Error Correction Coding in W-CDMA;39
4.6.3;1.6.3 Digital Video Broadcasting Channel Coding;39
4.6.4;1.6.4 Error Correction Coding in GPS L5 Signal;39
4.7;References;40
5;2 Overview of the Performance of Digital Communication Over Fading Channels;41
5.1;2.1 BER Performance of Different Modulation Schemes in AWGN, Rayleigh, and Rician Fading Channels;41
5.1.1;2.1.1 BER of BPSK Modulation in AWGN Channel;42
5.1.2;2.1.2 BER of BPSK Modulation in Rayleigh Fading Channel;43
5.1.3;2.1.3 BER of BPSK Modulation in Rician Fading Channel;44
5.1.4;2.1.4 BER Performance of BFSK in AWGN, Rayleigh, and Rician Fading Channels;45
5.1.5;2.1.5 Comparison of BER Performance of BPSK, QPSK, and 16-QAM in AWGN and Rayleigh Fading Channels;47
5.2;2.2 Wireless Communication Techniques;48
5.2.1;2.2.1 DS-CDMA;49
5.2.2;2.2.2 FH-CDMA;52
5.2.3;2.2.3 OFDM;55
5.2.4;2.2.4 MC-CDMA;59
5.3;2.3 Diversity Reception;62
5.3.1;2.3.1 Receive Diversity with N Receive Antennas in AWGN;63
5.4;2.4 Diversity Combining Techniques;64
5.4.1;2.4.1 Selection Diversity;64
5.4.2;2.4.2 Equal Gain Combining (EGC);65
5.4.3;2.4.3 Maximum Ratio Combining (MRC);66
5.5;2.5 Problems;70
5.6;2.6 MATLAB Exercises;70
5.7;References;71
6;3 Galois Field Theory;72
6.1;3.1 Set;72
6.2;3.2 Group;72
6.3;3.3 Field;73
6.4;3.4 Vector Spaces;74
6.5;3.5 Elementary Properties of Galois Fields;76
6.6;3.6 Galois Field Arithmetic;76
6.6.1;3.6.1 Addition and Subtraction of Polynomials;76
6.6.2;3.6.2 Multiplication of Polynomials;77
6.6.3;3.6.3 Multiplication of Polynomials Using MATLAB;77
6.6.4;3.6.4 Division of Polynomials;77
6.6.5;3.6.5 Division of Polynomials Using MATLAB;78
6.7;3.7 Polynomials Over Galois Fields;79
6.7.1;3.7.1 Irreducible Polynomial;79
6.7.2;3.7.2 Primitive Polynomials;80
6.7.3;3.7.3 Checking of Polynomials for Primitiveness Using MATLAB;80
6.7.4;3.7.4 Generation of Primitive Polynomials Using MATLAB;81
6.8;3.8 Construction of Galois Field GF( 2m ) from GF(2);81
6.8.1;3.8.1 Construction of GF( 2m ), Using MATLAB;87
6.9;3.9 Minimal Polynomials and Conjugacy Classes of GF( 2m );87
6.9.1;3.9.1 Minimal Polynomials;87
6.9.2;3.9.2 Conjugates of GF Elements;90
6.9.3;3.9.3 Properties of Minimal Polynomial;90
6.9.4;3.9.4 Construction of Minimal Polynomials;91
6.9.5;3.9.5 Construction of Conjugacy Classes Using MATLAB;93
6.9.6;3.9.6 Construction of Minimal Polynomials Using MATLAB;93
6.10;3.10 Problems;94
7;4 Linear Block Codes;95
7.1;4.1 Block Codes;95
7.2;4.2 Linear Block Codes;97
7.2.1;4.2.1 Linear Block Code Properties;97
7.2.2;4.2.2 Generator and Parity Check Matrices;98
7.2.3;4.2.3 Weight Distribution of Linear Block Codes;100
7.2.4;4.2.4 Hamming Codes;101
7.2.5;4.2.5 Syndrome Table Decoding;103
7.2.6;4.2.6 Hamming Codes Decoding;104
7.3;4.3 Cyclic Codes;105
7.3.1;4.3.1 The Basic Properties of Cyclic Codes;106
7.3.2;4.3.2 Encoding Algorithm for an ( n,k ) Cyclic Codes;107
7.3.3;4.3.3 Encoder for Cyclic Codes Using Shift Registers;109
7.3.4;4.3.4 Shift Register Encoders for Cyclic Codes;110
7.3.5;4.3.5 Cyclic Redundancy Check Codes;112
7.4;4.4 BCH Codes;114
7.4.1;4.4.1 BCH Code Design;114
7.4.2;4.4.2 Berlekamp’s Algorithm for Binary BCH Codes Decoding;120
7.4.3;4.4.3 Chien Search Algorithm;121
7.5;4.5 Reed–Solomon Codes;125
7.5.1;4.5.1 Reed–Solomon Encoder;126
7.5.2;4.5.2 Decoding of Reed–Solomon Codes;128
7.5.3;4.5.3 Binary Erasure Decoding;139
7.5.4;4.5.4 Non-binary Erasure Decoding;139
7.6;4.6 Performance Analysis of RS Codes;143
7.6.1;4.6.1 BER Performance of RS Codes for BPSK Modulation in AWGN and Rayleigh Fading Channels;143
7.6.2;4.6.2 BER Performance of RS Codes for Non-coherent BFSK Modulation in AWGN and Rayleigh Fading Channels;147
7.7;4.7 Problems;149
7.8;4.8 MATLAB Exercises;150
7.9;References;151
8;5 Convolutional Codes;152
8.1;5.1 Structure of Non-systematic Convolutional Encoder;152
8.1.1;5.1.1 Impulse Response of Convolutional Codes;154
8.1.2;5.1.2 Constraint Length;156
8.1.3;5.1.3 Convolutional Encoding Using MATLAB;156
8.2;5.2 Structure of Systematic Convolutional Encoder;157
8.3;5.3 The Structural Properties of Convolutional Codes;157
8.3.1;5.3.1 State Diagram;157
8.3.2;5.3.2 Catastrophic Convolutional Codes;157
8.3.3;5.3.3 Transfer Function of a Convolutional Encoder;159
8.3.4;5.3.4 Distance Properties of Convolutional Codes;163
8.3.5;5.3.5 Trellis Diagram;163
8.4;5.4 Punctured Convolutional Codes;169
8.5;5.5 The Viterbi Decoding Algorithm;170
8.5.1;5.5.1 Hard Decision Decoding;171
8.5.2;5.5.2 Soft Decision Decoding;173
8.6;5.6 Performance Analysis of Convolutional Codes;178
8.6.1;5.6.1 Binary Symmetric Channel;178
8.6.2;5.6.2 AWGN Channel;180
8.6.3;5.6.3 Rayleigh Fading Channel;182
8.7;5.7 Tail-Biting Convolutional Code;184
8.7.1;5.7.1 Tail-Biting Encoding;185
8.7.2;5.7.2 Tail-Biting Encoding Using MATLAB;186
8.7.3;5.7.3 Tail-Biting Decoding;187
8.8;5.8 Performance Analysis of Tail-Biting Convolutional Codes;188
8.9;5.9 Problems;192
8.10;5.10 MATLAB Exercises;194
8.11;References;194
9;6 Turbo Codes;195
9.1;6.1 Non-recursive and Recursive Systematic Convolutional Encoders;195
9.1.1;6.1.1 Recursive Systematic Convolutional (RSC) Encoder;196
9.2;6.2 Turbo Encoder;197
9.2.1;6.2.1 Different Types of Interleavers;198
9.2.2;6.2.2 Turbo Coding Illustration;199
9.2.3;6.2.3 Turbo Coding Using MATLAB;203
9.2.4;6.2.4 Encoding Tail-Biting Codes with RSC (Feedback) Encoders;210
9.3;6.3 Turbo Decoder;213
9.3.1;6.3.1 The BCJR Algorithm;215
9.3.2;6.3.2 Turbo Decoding Illustration;219
9.3.3;6.3.3 Convergence Behavior of the Turbo Codes;227
9.3.4;6.3.4 EXIT Analysis of Turbo Codes;228
9.4;6.4 Performance Analysis of the Turbo Codes;231
9.4.1;6.4.1 Upper Bound for the Turbo Codes in AWGN Channel;231
9.4.2;6.4.2 Upper Bound for Turbo Codes in Rayleigh Fading Channel;232
9.4.3;6.4.3 Effect of Free Distance on the Performance of the Turbo Codes;236
9.4.4;6.4.4 Effect of Number of Iterations on the Performance of the Turbo Codes;238
9.4.5;6.4.5 Effect of Puncturing on the Performance of the Turbo Codes;239
9.5;6.5 Enhanced Turbo Codes;239
9.5.1;6.5.1 Enhanced Turbo Encoder;240
9.5.2;6.5.2 Enhanced List Turbo Decoder;240
9.6;6.6 Performance Analysis of Enhanced Turbo Codes;240
9.6.1;6.6.1 Performance of Enhanced Tail-Biting Turbo Codes Over AWGN and Rayleigh Fading Channels;240
9.6.2;6.6.2 Performance of Enhanced Turbo Codes with Tail-Biting List Decoding in AWGN Channels;242
9.7;6.7 Problems;243
9.8;6.8 MATLAB Exercises;244
9.9;References;244
10;7 Bandwidth Efficient Coded Modulation;246
10.1;7.1 Set Partitioning;247
10.2;7.2 Design of the TCM Scheme;248
10.3;7.3 Decoding TCM;254
10.4;7.4 TCM Performance Analysis;254
10.4.1;7.4.1 Asymptotic Coding Gain;254
10.4.2;7.4.2 Bit Error Rate;255
10.4.3;7.4.3 Simulation of the BER Performance of a 8-State 8-PSK TCM in the AWGN and Rayleigh Fading Channels Using MATLAB;263
10.5;7.5 Turbo Trellis-Coded Modulation (TTCM);267
10.5.1;7.5.1 TTCM Encoder;267
10.5.2;7.5.2 TTCM Decoder;268
10.5.3;7.5.3 Simulation of the BER Performance of the 8-State 8-PSK TTCM in AWGN and Rayleigh Fading Channels;270
10.6;7.6 Bit-Interleaved Coded Modulation;271
10.6.1;7.6.1 BICM Encoder;272
10.6.2;7.6.2 BICM Decoder;275
10.7;7.7 Bit-Interleaved Coded Modulation Using Iterative Decoding;276
10.7.1;7.7.1 BICM-ID Encoder and Decoder;276
10.7.2;7.7.2 Simulation of the BER Performance of 8-State 8-PSK BICM and BICM-ID in AWGN and Rayleigh Fading Channels;277
10.8;7.8 Problems;278
10.9;Appendix A;280
10.10;References;285
11;8 Low Density Parity Check Codes;286
11.1;8.1 LDPC Code Properties;286
11.2;8.2 Construction of Parity Check Matrix H;287
11.2.1;8.2.1 Gallager Method for Random Construction of H for Regular Codes;287
11.2.2;8.2.2 Algebraic Construction of H for Regular Codes;288
11.2.3;8.2.3 Random Construction of H for Irregular Codes;289
11.3;8.3 Representation of Parity Check Matrix Using Tanner Graphs;290
11.3.1;8.3.1 Cycles of Tanner Graph;291
11.3.2;8.3.2 Detection and Removal of Girth 4 of a Parity Check Matrix;292
11.4;8.4 LDPC Encoding;295
11.4.1;8.4.1 Preprocessing Method;295
11.5;8.5 Efficient Encoding of LDPC Codes;301
11.5.1;8.5.1 Efficient Encoding of LDPC Codes Using MATLAB;304
11.6;8.6 LDPC Decoding;305
11.6.1;8.6.1 LDPC Decoding on Binary Erasure Channel Using Message Passing Algorithm;305
11.6.2;8.6.2 LDPC Decoding on Binary Erasure Channel Using MATLAB;307
11.6.3;8.6.3 Bit-Flipping Decoding Algorithm;310
11.6.4;8.6.4 Bit-Flipping Decoding Using MATLAB;312
11.7;8.7 Sum Product Decoding;314
11.7.1;8.7.1 Log Domain Sum-Product Algorithm (SPA);318
11.7.2;8.7.2 The Min-Sum Algorithm;319
11.7.3;8.7.3 Sum Product and Min-Sum Algorithms for Decoding of Rate 1/2 LDPC Codes Using MATLAB;322
11.8;8.8 EXIT Analysis of LDPC Codes;325
11.8.1;8.8.1 Degree Distribution;325
11.8.2;8.8.2 Ensemble Decoding Thresholds;326
11.8.3;8.8.3 EXIT Charts for Irregular LDPC Codes in Binary Input AWGN Channels;327
11.9;8.9 Performance Analysis of LDPC Codes;329
11.9.1;8.9.1 Performance Comparison of Sum-Product and Min-Sum Algorithms for Decoding of Regular LDPC Codes in AWGN Channel;329
11.9.2;8.9.2 BER Performance Comparison of Regular and Irregular LDPC Codes in AWGN Channel;330
11.9.3;8.9.3 Effect of Block Length on the BER Performance of LDPC Codes in AWGN Channel;330
11.9.4;8.9.4 Error Floor Comparison of Irregular LDPC Codes of Different Degree Distribution in AWGN Channel;332
11.10;8.10 Quasi Cyclic (QC)-LDPC CODES;333
11.10.1;8.10.1 Brief Description of QC-LDPC Codes;333
11.10.2;8.10.2 Base Matrix and Expansion;334
11.10.3;8.10.3 Performance Analysis of QC-LDPC Codes Over AWGN Channel;335
11.11;8.11 Problems;339
11.12;8.12 MATLAB Exercises;341
11.13;References;341
12;9 LT and Raptor Codes;343
12.1;9.1 LT Codes Design;343
12.1.1;9.1.1 LT Degree Distributions;344
12.1.2;9.1.2 Important Properties of the Robust Soliton Distribution;345
12.1.3;9.1.3 LT Encoder;346
12.1.4;9.1.4 Tanner Graph of LT Codes;347
12.1.5;9.1.5 LT Decoding with Hard Decision;347
12.1.6;9.1.6 Hard Decision LT Decoding Using MATLAB;350
12.1.7;9.1.7 BER Performance of LT Decoding Over BEC Using MATLAB;351
12.2;9.2 Systematic LT Codes;353
12.2.1;9.2.1 Systematic LT Codes Decoding;354
12.2.2;9.2.2 BER Performance Analysis of Systematic LT Codes Using MATLAB;354
12.3;9.3 Raptor Codes;358
12.4;9.4 Problems;360
12.5;9.5 MATLAB Exercises;360
12.6;References;360
13;10 Polar Codes;362
13.1;10.1 Channel Polarization;362
13.1.1;10.1.1 Channel Combining Phase;363
13.1.2;10.1.2 Channel Splitting Phase;368
13.1.3;10.1.3 Polarization of Binary Erasure Channels;369
13.1.4;10.1.4 Polarization Theorem;372
13.1.5;10.1.5 Polarization of AWGN Channels;373
13.2;10.2 Polar Encoder Structures and Encoding;373
13.2.1;10.2.1 Polar Encoder for N = 2;374
13.2.2;10.2.2 Polar Encoder for N = 4;374
13.2.3;10.2.3 Polar Encoder for N = 4 with Input Data Vector Permuted;375
13.2.4;10.2.4 Polar Encoder for N = 8;375
13.2.5;10.2.5 Polar Encoder for N = 8 with Input Data Vector Permuted;376
13.2.6;10.2.6 Non-systematic Polar Encoding Using MATLAB;378
13.2.7;10.2.7 Systematic Polar Encoding;379
13.2.8;10.2.8 Efficient Systematic Polar Encoding Algorithm;380
13.3;10.3 Polar Decoding;382
13.3.1;10.3.1 Successive Cancelation Decoding;382
13.3.2;10.3.2 SC Decoding Algorithm;385
13.3.3;10.3.3 Successive Cancelation List Decoding;392
13.4;10.4 Problems;392
13.5;10.5 MATLAB Exercises;393
13.6;References;394
14;11 MIMO System;395
14.1;11.1 What Is MIMO?;395
14.2;11.2 MIMO Channel Model;395
14.2.1;11.2.1 The Frequency Flat MIMO Channel;395
14.2.2;11.2.2 The Frequency-Selective MIMO Channel;397
14.2.3;11.2.3 MIMO-OFDM System;397
14.3;11.3 Channel Estimation;398
14.3.1;11.3.1 LS Channel Estimation;399
14.3.2;11.3.2 DFT-Based Channel Estimation;399
14.3.3;11.3.3 MIMO-OFDM Channel Estimation Using LS;400
14.3.4;11.3.4 Channel Estimation Using MATLAB;400
14.4;11.4 MIMO Channel Decomposition;402
14.5;11.5 MIMO Channel Capacity;409
14.5.1;11.5.1 Capacity of Deterministic MIMO Channel When CSI Is Known to the Transmitter;409
14.5.2;11.5.2 Deterministic MIMO Channel Capacity When CSI Is Unknown at the Transmitter;411
14.5.3;11.5.3 Random MIMO Channel Capacity;413
14.6;11.6 MIMO-OFDM Channel Estimation Using OMP Algorithm;421
14.6.1;11.6.1 OMP Algorithm;422
14.7;11.7 MIMO Channel Equalization;426
14.7.1;11.7.1 Zero Forcing (ZF) Equalization;427
14.7.2;11.7.2 Minimum Mean Square Error (MMSE) Equalization;428
14.8;11.8 Problems;429
14.9;11.9 MATLAB Exercises;430
14.10;References;431
15;12 Space-Time Coding;432
15.1;12.1 Space-Time-Coded MIMO System;432
15.2;12.2 Space-Time Block Code (STBC);433
15.2.1;12.2.1 Rate Limit;433
15.2.2;12.2.2 Orthogonality;434
15.2.3;12.2.3 Diversity Criterion;434
15.2.4;12.2.4 Performance Criteria;435
15.2.5;12.2.5 Decoding STBCs;436
15.3;12.3 Alamouti Code;436
15.3.1;12.3.1 2-Transmit, 1-Receive Alamouti STBC Coding;437
15.3.2;12.3.2 2-Transmit, 2-Receive Alamouti STBC Coding;438
15.3.3;12.3.3 Theoretical BER Performance of BPSK Alamouti Codes Using MATLAB;442
15.4;12.4 Higher-Order STBCs;443
15.4.1;12.4.1 3-Transmit, 4-Receive STBC Coding;444
15.4.2;12.4.2 Simulation of BER Performance of STBCs Using MATLAB;448
15.5;12.5 Space-Time Trellis Coding;451
15.5.1;12.5.1 Space-Time Trellis Encoder;452
15.5.2;12.5.2 Simulation of BER Performance of 4-state QPSK STTC Using MATLAB;460
15.6;12.6 MIMO-OFDM Implementation;466
15.6.1;12.6.1 Space-Time-Coded OFDM;468
15.6.2;12.6.2 Space-Frequency Coded OFDM;468
15.6.3;12.6.3 Space-Time-Frequency Coded OFDM;469
15.7;12.7 Problems;470
15.8;12.8 MATLAB Exercises;472
15.9;References;472
16;13 Channel Codes Evolution for 5G;473
16.1;13.1 5G Requirements;473
16.2;13.2 QC-LDPC and Polar Codes for eMBB;474
16.2.1;13.2.1 Performance Evaluation of QC-LDPC Codes for eMBB Data Channel;475
16.2.2;13.2.2 Performance Evaluation of Polar Codes for eMBB Control Channel;476
16.3;13.3 Evaluation of Enhanced Turbo Codes and Polar Codes for URLLC;478
16.3.1;13.3.1 Decoding Latency;481
16.3.2;13.3.2 Decoding Complexity;482
16.4;13.4 Channel Codes for mMTC;482
16.5;References;484