Channel Coding Techniques for Wireless Communications (eBook)
XIX, 476 Seiten
Springer Singapore (Verlag)
978-981-15-0561-4 (ISBN)
K. Deergha Rao is Professor at the Department of Electronics and Communication Engineering, Vasavi College of Engineering, Osmania University, Hyderabad, India. He is former Director and Professor of Research and Training Unit for Navigational Electronics (NERTU), Osmania University. He was a postdoctoral fellow and part-time professor for four years at the Department of Electronics and Communication Engineering, Concordia University, Montreal, Canada. His teaching areas are signals and systems, digital signal processing, channel coding techniques, and MIMO communication systems. Professor Rao has executed research projects for premium Indian organizations such as DRDO, HAL, and BEL and is interested in research areas of wireless channel coding, MIMO-OFDM communications, image processing, cryptosystems, and VLSI signal processing. He has also served as the founder chairman of the joint chapter between IEEE Communications Society and IEEE Signal Processing Society in Hyderabad from 2010-2012 and communications track chair for IEEE INDICON 2011 held in Hyderabad. Five students have been so far awarded Ph.D. degrees under Professor Rao, while three are currently working towards their Ph.D.
An awardee of the IETE K. S. Krishnan Memorial Award for the best system oriented paper in 2013, Prof. Rao has presented papers at IEEE International conferences several times in the USA, Switzerland, Russia, and Thailand. He has more than 100 publications to his credit including more than 60 publications in the IEEE journals and conference proceedings. Professor Rao is the author of two books-Channel Coding Techniques for Wireless Communications (Springer, 2015) and Signals and Systems (Springer, 2018)-and has co-authored Digital Signal Processing (Jaico Publishing House, 2012) and Digital Signal Processing: Theory and Practice (Springer, 2018). He is an editorial board member for the International Journal of Sustainable Aviation.
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.
Preface 7
Contents 9
About the Author 19
1 Introduction 20
1.1 Digital Communication System 20
1.2 Wireless Communication Channels 21
1.2.1 Binary Erasure Channel (BEC) 21
1.2.2 Binary Symmetric Channel (BSC) 22
1.2.3 Additive White Gaussian Noise Channel 22
1.2.4 Gilbert–Elliott Channel 23
1.2.5 Fading Channel 24
1.2.6 Fading 24
1.3 Statistical Models for Fading Channels 27
1.3.1 Probability Density Function of Rician Fading Channel 27
1.3.2 Probability Density Function of Rayleigh Fading Channel 28
1.3.3 Probability Density Function of Nakagami Fading Channel 28
1.4 Channel Capacity 29
1.4.1 Channel Capacity of Binary Erasure Channel 30
1.4.2 Channel Capacity of Binary Symmetric Channel 30
1.4.3 Capacity of AWGN Channel 30
1.4.4 Channel Capacity of Gilbert–Elliott Channels 32
1.4.5 Ergodic Capacity of Fading Channels 32
1.4.6 Outage Probability of a Fading Channel 34
1.4.7 Outage Capacity of Fading Channels 35
1.4.8 Capacity of Fading Channels with CSI at the Transmitter and Receiver 36
1.5 Channel Coding for Improving the Performance of Communication System 36
1.5.1 Shannon’s Noisy Channel Coding Theorem 36
1.5.2 Channel Coding Principle 37
1.5.3 Channel Coding Gain 37
1.6 Some Application Examples of Channel Coding 38
1.6.1 Error Correction Coding in GSM 38
1.6.2 Error Correction Coding in W-CDMA 39
1.6.3 Digital Video Broadcasting Channel Coding 39
1.6.4 Error Correction Coding in GPS L5 Signal 39
References 40
2 Overview of the Performance of Digital Communication Over Fading Channels 41
2.1 BER Performance of Different Modulation Schemes in AWGN, Rayleigh, and Rician Fading Channels 41
2.1.1 BER of BPSK Modulation in AWGN Channel 42
2.1.2 BER of BPSK Modulation in Rayleigh Fading Channel 43
2.1.3 BER of BPSK Modulation in Rician Fading Channel 44
2.1.4 BER Performance of BFSK in AWGN, Rayleigh, and Rician Fading Channels 45
2.1.5 Comparison of BER Performance of BPSK, QPSK, and 16-QAM in AWGN and Rayleigh Fading Channels 47
2.2 Wireless Communication Techniques 48
2.2.1 DS-CDMA 49
2.2.2 FH-CDMA 52
2.2.3 OFDM 55
2.2.4 MC-CDMA 59
2.3 Diversity Reception 62
2.3.1 Receive Diversity with N Receive Antennas in AWGN 63
2.4 Diversity Combining Techniques 64
2.4.1 Selection Diversity 64
2.4.2 Equal Gain Combining (EGC) 65
2.4.3 Maximum Ratio Combining (MRC) 66
2.5 Problems 70
2.6 MATLAB Exercises 70
References 71
3 Galois Field Theory 72
3.1 Set 72
3.2 Group 72
3.3 Field 73
3.4 Vector Spaces 74
3.5 Elementary Properties of Galois Fields 76
3.6 Galois Field Arithmetic 76
3.6.1 Addition and Subtraction of Polynomials 76
3.6.2 Multiplication of Polynomials 77
3.6.3 Multiplication of Polynomials Using MATLAB 77
3.6.4 Division of Polynomials 77
3.6.5 Division of Polynomials Using MATLAB 78
3.7 Polynomials Over Galois Fields 79
3.7.1 Irreducible Polynomial 79
3.7.2 Primitive Polynomials 80
3.7.3 Checking of Polynomials for Primitiveness Using MATLAB 80
3.7.4 Generation of Primitive Polynomials Using MATLAB 81
3.8 Construction of Galois Field GF( 2m ) from GF(2) 81
3.8.1 Construction of GF( 2m ), Using MATLAB 87
3.9 Minimal Polynomials and Conjugacy Classes of GF( 2m ) 87
3.9.1 Minimal Polynomials 87
3.9.2 Conjugates of GF Elements 90
3.9.3 Properties of Minimal Polynomial 90
3.9.4 Construction of Minimal Polynomials 91
3.9.5 Construction of Conjugacy Classes Using MATLAB 93
3.9.6 Construction of Minimal Polynomials Using MATLAB 93
3.10 Problems 94
4 Linear Block Codes 95
4.1 Block Codes 95
4.2 Linear Block Codes 97
4.2.1 Linear Block Code Properties 97
4.2.2 Generator and Parity Check Matrices 98
4.2.3 Weight Distribution of Linear Block Codes 100
4.2.4 Hamming Codes 101
4.2.5 Syndrome Table Decoding 103
4.2.6 Hamming Codes Decoding 104
4.3 Cyclic Codes 105
4.3.1 The Basic Properties of Cyclic Codes 106
4.3.2 Encoding Algorithm for an ( n,k ) Cyclic Codes 107
4.3.3 Encoder for Cyclic Codes Using Shift Registers 109
4.3.4 Shift Register Encoders for Cyclic Codes 110
4.3.5 Cyclic Redundancy Check Codes 112
4.4 BCH Codes 114
4.4.1 BCH Code Design 114
4.4.2 Berlekamp’s Algorithm for Binary BCH Codes Decoding 120
4.4.3 Chien Search Algorithm 121
4.5 Reed–Solomon Codes 125
4.5.1 Reed–Solomon Encoder 126
4.5.2 Decoding of Reed–Solomon Codes 128
4.5.3 Binary Erasure Decoding 139
4.5.4 Non-binary Erasure Decoding 139
4.6 Performance Analysis of RS Codes 143
4.6.1 BER Performance of RS Codes for BPSK Modulation in AWGN and Rayleigh Fading Channels 143
4.6.2 BER Performance of RS Codes for Non-coherent BFSK Modulation in AWGN and Rayleigh Fading Channels 147
4.7 Problems 149
4.8 MATLAB Exercises 150
References 151
5 Convolutional Codes 152
5.1 Structure of Non-systematic Convolutional Encoder 152
5.1.1 Impulse Response of Convolutional Codes 154
5.1.2 Constraint Length 156
5.1.3 Convolutional Encoding Using MATLAB 156
5.2 Structure of Systematic Convolutional Encoder 157
5.3 The Structural Properties of Convolutional Codes 157
5.3.1 State Diagram 157
5.3.2 Catastrophic Convolutional Codes 157
5.3.3 Transfer Function of a Convolutional Encoder 159
5.3.4 Distance Properties of Convolutional Codes 163
5.3.5 Trellis Diagram 163
5.4 Punctured Convolutional Codes 169
5.5 The Viterbi Decoding Algorithm 170
5.5.1 Hard Decision Decoding 171
5.5.2 Soft Decision Decoding 173
5.6 Performance Analysis of Convolutional Codes 178
5.6.1 Binary Symmetric Channel 178
5.6.2 AWGN Channel 180
5.6.3 Rayleigh Fading Channel 182
5.7 Tail-Biting Convolutional Code 184
5.7.1 Tail-Biting Encoding 185
5.7.2 Tail-Biting Encoding Using MATLAB 186
5.7.3 Tail-Biting Decoding 187
5.8 Performance Analysis of Tail-Biting Convolutional Codes 188
5.9 Problems 192
5.10 MATLAB Exercises 194
References 194
6 Turbo Codes 195
6.1 Non-recursive and Recursive Systematic Convolutional Encoders 195
6.1.1 Recursive Systematic Convolutional (RSC) Encoder 196
6.2 Turbo Encoder 197
6.2.1 Different Types of Interleavers 198
6.2.2 Turbo Coding Illustration 199
6.2.3 Turbo Coding Using MATLAB 203
6.2.4 Encoding Tail-Biting Codes with RSC (Feedback) Encoders 210
6.3 Turbo Decoder 213
6.3.1 The BCJR Algorithm 215
6.3.2 Turbo Decoding Illustration 219
6.3.3 Convergence Behavior of the Turbo Codes 227
6.3.4 EXIT Analysis of Turbo Codes 228
6.4 Performance Analysis of the Turbo Codes 231
6.4.1 Upper Bound for the Turbo Codes in AWGN Channel 231
6.4.2 Upper Bound for Turbo Codes in Rayleigh Fading Channel 232
6.4.3 Effect of Free Distance on the Performance of the Turbo Codes 236
6.4.4 Effect of Number of Iterations on the Performance of the Turbo Codes 238
6.4.5 Effect of Puncturing on the Performance of the Turbo Codes 239
6.5 Enhanced Turbo Codes 239
6.5.1 Enhanced Turbo Encoder 240
6.5.2 Enhanced List Turbo Decoder 240
6.6 Performance Analysis of Enhanced Turbo Codes 240
6.6.1 Performance of Enhanced Tail-Biting Turbo Codes Over AWGN and Rayleigh Fading Channels 240
6.6.2 Performance of Enhanced Turbo Codes with Tail-Biting List Decoding in AWGN Channels 242
6.7 Problems 243
6.8 MATLAB Exercises 244
References 244
7 Bandwidth Efficient Coded Modulation 246
7.1 Set Partitioning 247
7.2 Design of the TCM Scheme 248
7.3 Decoding TCM 254
7.4 TCM Performance Analysis 254
7.4.1 Asymptotic Coding Gain 254
7.4.2 Bit Error Rate 255
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
7.5 Turbo Trellis-Coded Modulation (TTCM) 267
7.5.1 TTCM Encoder 267
7.5.2 TTCM Decoder 268
7.5.3 Simulation of the BER Performance of the 8-State 8-PSK TTCM in AWGN and Rayleigh Fading Channels 270
7.6 Bit-Interleaved Coded Modulation 271
7.6.1 BICM Encoder 272
7.6.2 BICM Decoder 275
7.7 Bit-Interleaved Coded Modulation Using Iterative Decoding 276
7.7.1 BICM-ID Encoder and Decoder 276
7.7.2 Simulation of the BER Performance of 8-State 8-PSK BICM and BICM-ID in AWGN and Rayleigh Fading Channels 277
7.8 Problems 278
Appendix A 280
References 285
8 Low Density Parity Check Codes 286
8.1 LDPC Code Properties 286
8.2 Construction of Parity Check Matrix H 287
8.2.1 Gallager Method for Random Construction of H for Regular Codes 287
8.2.2 Algebraic Construction of H for Regular Codes 288
8.2.3 Random Construction of H for Irregular Codes 289
8.3 Representation of Parity Check Matrix Using Tanner Graphs 290
8.3.1 Cycles of Tanner Graph 291
8.3.2 Detection and Removal of Girth 4 of a Parity Check Matrix 292
8.4 LDPC Encoding 295
8.4.1 Preprocessing Method 295
8.5 Efficient Encoding of LDPC Codes 301
8.5.1 Efficient Encoding of LDPC Codes Using MATLAB 304
8.6 LDPC Decoding 305
8.6.1 LDPC Decoding on Binary Erasure Channel Using Message Passing Algorithm 305
8.6.2 LDPC Decoding on Binary Erasure Channel Using MATLAB 307
8.6.3 Bit-Flipping Decoding Algorithm 310
8.6.4 Bit-Flipping Decoding Using MATLAB 312
8.7 Sum Product Decoding 314
8.7.1 Log Domain Sum-Product Algorithm (SPA) 318
8.7.2 The Min-Sum Algorithm 319
8.7.3 Sum Product and Min-Sum Algorithms for Decoding of Rate 1/2 LDPC Codes Using MATLAB 322
8.8 EXIT Analysis of LDPC Codes 325
8.8.1 Degree Distribution 325
8.8.2 Ensemble Decoding Thresholds 326
8.8.3 EXIT Charts for Irregular LDPC Codes in Binary Input AWGN Channels 327
8.9 Performance Analysis of LDPC Codes 329
8.9.1 Performance Comparison of Sum-Product and Min-Sum Algorithms for Decoding of Regular LDPC Codes in AWGN Channel 329
8.9.2 BER Performance Comparison of Regular and Irregular LDPC Codes in AWGN Channel 330
8.9.3 Effect of Block Length on the BER Performance of LDPC Codes in AWGN Channel 330
8.9.4 Error Floor Comparison of Irregular LDPC Codes of Different Degree Distribution in AWGN Channel 332
8.10 Quasi Cyclic (QC)-LDPC CODES 333
8.10.1 Brief Description of QC-LDPC Codes 333
8.10.2 Base Matrix and Expansion 334
8.10.3 Performance Analysis of QC-LDPC Codes Over AWGN Channel 335
8.11 Problems 339
8.12 MATLAB Exercises 341
References 341
9 LT and Raptor Codes 343
9.1 LT Codes Design 343
9.1.1 LT Degree Distributions 344
9.1.2 Important Properties of the Robust Soliton Distribution 345
9.1.3 LT Encoder 346
9.1.4 Tanner Graph of LT Codes 347
9.1.5 LT Decoding with Hard Decision 347
9.1.6 Hard Decision LT Decoding Using MATLAB 350
9.1.7 BER Performance of LT Decoding Over BEC Using MATLAB 351
9.2 Systematic LT Codes 353
9.2.1 Systematic LT Codes Decoding 354
9.2.2 BER Performance Analysis of Systematic LT Codes Using MATLAB 354
9.3 Raptor Codes 358
9.4 Problems 360
9.5 MATLAB Exercises 360
References 360
10 Polar Codes 362
10.1 Channel Polarization 362
10.1.1 Channel Combining Phase 363
10.1.2 Channel Splitting Phase 368
10.1.3 Polarization of Binary Erasure Channels 369
10.1.4 Polarization Theorem 372
10.1.5 Polarization of AWGN Channels 373
10.2 Polar Encoder Structures and Encoding 373
10.2.1 Polar Encoder for N = 2 374
10.2.2 Polar Encoder for N = 4 374
10.2.3 Polar Encoder for N = 4 with Input Data Vector Permuted 375
10.2.4 Polar Encoder for N = 8 375
10.2.5 Polar Encoder for N = 8 with Input Data Vector Permuted 376
10.2.6 Non-systematic Polar Encoding Using MATLAB 378
10.2.7 Systematic Polar Encoding 379
10.2.8 Efficient Systematic Polar Encoding Algorithm 380
10.3 Polar Decoding 382
10.3.1 Successive Cancelation Decoding 382
10.3.2 SC Decoding Algorithm 385
10.3.3 Successive Cancelation List Decoding 392
10.4 Problems 392
10.5 MATLAB Exercises 393
References 394
11 MIMO System 395
11.1 What Is MIMO? 395
11.2 MIMO Channel Model 395
11.2.1 The Frequency Flat MIMO Channel 395
11.2.2 The Frequency-Selective MIMO Channel 397
11.2.3 MIMO-OFDM System 397
11.3 Channel Estimation 398
11.3.1 LS Channel Estimation 399
11.3.2 DFT-Based Channel Estimation 399
11.3.3 MIMO-OFDM Channel Estimation Using LS 400
11.3.4 Channel Estimation Using MATLAB 400
11.4 MIMO Channel Decomposition 402
11.5 MIMO Channel Capacity 409
11.5.1 Capacity of Deterministic MIMO Channel When CSI Is Known to the Transmitter 409
11.5.2 Deterministic MIMO Channel Capacity When CSI Is Unknown at the Transmitter 411
11.5.3 Random MIMO Channel Capacity 413
11.6 MIMO-OFDM Channel Estimation Using OMP Algorithm 421
11.6.1 OMP Algorithm 422
11.7 MIMO Channel Equalization 426
11.7.1 Zero Forcing (ZF) Equalization 427
11.7.2 Minimum Mean Square Error (MMSE) Equalization 428
11.8 Problems 429
11.9 MATLAB Exercises 430
References 431
12 Space-Time Coding 432
12.1 Space-Time-Coded MIMO System 432
12.2 Space-Time Block Code (STBC) 433
12.2.1 Rate Limit 433
12.2.2 Orthogonality 434
12.2.3 Diversity Criterion 434
12.2.4 Performance Criteria 435
12.2.5 Decoding STBCs 436
12.3 Alamouti Code 436
12.3.1 2-Transmit, 1-Receive Alamouti STBC Coding 437
12.3.2 2-Transmit, 2-Receive Alamouti STBC Coding 438
12.3.3 Theoretical BER Performance of BPSK Alamouti Codes Using MATLAB 442
12.4 Higher-Order STBCs 443
12.4.1 3-Transmit, 4-Receive STBC Coding 444
12.4.2 Simulation of BER Performance of STBCs Using MATLAB 448
12.5 Space-Time Trellis Coding 451
12.5.1 Space-Time Trellis Encoder 452
12.5.2 Simulation of BER Performance of 4-state QPSK STTC Using MATLAB 460
12.6 MIMO-OFDM Implementation 466
12.6.1 Space-Time-Coded OFDM 468
12.6.2 Space-Frequency Coded OFDM 468
12.6.3 Space-Time-Frequency Coded OFDM 469
12.7 Problems 470
12.8 MATLAB Exercises 472
References 472
13 Channel Codes Evolution for 5G 473
13.1 5G Requirements 473
13.2 QC-LDPC and Polar Codes for eMBB 474
13.2.1 Performance Evaluation of QC-LDPC Codes for eMBB Data Channel 475
13.2.2 Performance Evaluation of Polar Codes for eMBB Control Channel 476
13.3 Evaluation of Enhanced Turbo Codes and Polar Codes for URLLC 478
13.3.1 Decoding Latency 481
13.3.2 Decoding Complexity 482
13.4 Channel Codes for mMTC 482
References 484
| Erscheint lt. Verlag | 22.11.2019 |
|---|---|
| Reihe/Serie | Forum for Interdisciplinary Mathematics | Forum for Interdisciplinary Mathematics |
| Zusatzinfo | XIX, 476 p. 381 illus., 81 illus. in color. |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Informatik ► Netzwerke |
| Informatik ► Theorie / Studium ► Kryptologie | |
| Mathematik / Informatik ► Informatik ► Web / Internet | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften | |
| Technik ► Elektrotechnik / Energietechnik | |
| Technik ► Nachrichtentechnik | |
| Schlagworte | Block Codes • coding theory • Information and Communication, Circuits • Low parity check code • PC-based MATLAB programs • Turbo Code • wireless communication |
| ISBN-10 | 981-15-0561-6 / 9811505616 |
| ISBN-13 | 978-981-15-0561-4 / 9789811505614 |
| Haben Sie eine Frage zum Produkt? |
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