ERROR CONTROL CODING Notes

Ravi Chopra | 24-Feb-2016 |

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Contents
PREFACE xiii
CHAPTER 1 CODING FOR REUABLE DIGITAL TRANSMISSION
AND STORAGE
I.I Introduction
1.2 Types of Codes 3
1.3 Modulation and Demodulation 5
1.4 Maximum Likelihood Decoding 8
1.5 Types of Errors 77
1.6 Error Control Strategies 12
References 14
CHAPTER 2 INTRODUCTION TO ALGEBRA 15
2.1 Groups 75
2.2 Fields 19
2.3 Binary Field Arithmetic 24
2.4 Construction of Galois Field GF(2m) 29
2.5 Basic Properties of Galois Field GF(2m) 34
2.6 Computations Using Galois Field GF(2m) Arithmetic 39
2.7 Vector Spaces 40
2.8 Matrices 46
Problems 48
References 50
vii
CHAPTER 3 UNEAR BLOCK CODES 51
3.1 Introduction to Linear Block Codes 57
3.2 Syndrome and Error Detection 58
3.3 Minimum Distance of a Block Code 63
3.4 Error-Detecting and Error-Correcting Capabilities
of a Block Code 65
3.5 Standard Array and Syndrome Decoding 68
3.6 Probability of an Undetected Error for Linear Codes
over a BSC 76
3. 7 Hamming Codes 79
Problems 82
References 84
CHAPTER 4 CYCUC CODES 85
4.1 Description of Cyclic Codes 85
4.2 Generator and Parity-Check Matrices of Cyclic Codes 92
4.3 Encoding of Cyclic Codes 95
4.4 Syndrome Computation and Error Detection 98
4.5 Decoding of Cyclic Codes 703
4.6 Cyclic Hamming Codes 111
4. 7 Shortened Cyclic Codes 776
Problems 727
References 7 2 3
CHAPTER 5 ERROR-TRAPPING DECODING FOR CYCUC
CODES 125
5.1 Error-Trapping Decoding 725
5.2 Improved Error-Trapping Decoding 737
5.3 The Golay Code 134
Problems 739
References 739
CHAPTER 6 BCH CODES 141
viii
6.1 Description of the Codes 142
6.2 Decoding of the BCH Codes 151
6.3 Implementation of Galois Field Arithmetic 767
6.4 Implementation of Error Correction 167
6.5 Nonbinary BCH Codes and Reed-Solomon Codes 170
6.6 Weight Distribution and Error Detection of Binary
BCH Codes 177
Problems
References
180
182
Contents
CHAPTER 7 MAJORJTY-LOGIC DECODING FOR CYCLIC
CODES 184
7.1 One-Step Majority-Logic Decoding 184
7.2 Class of One-Step Majority-Logic Decodable Codes 194
7.3 Other One-Step Majority-Logic Decodable Codes 201
7.4 Multiple-Step Majority-Logic Decoding 209
Problems 279
References 227
CHAPTER 8 FINITE GEOMETRY CODES 223
8.1 Euclidean Geometry 223
8.2 Majority-Logic Decodable Cyclic Codes Based
on Euclidean Geometry 227
8.3 Projective Geometry and Projective Geometry Codes 240
8.4 Modifications of Majority-Logic Decoding 245
Problems 253
References 255
CHAPTER 9 BURST-ERROR-CORRECTING CODES 257
9.1 Introduction 257
9.2 Decoding of Single-Burst-Error-Correcting Cyclic Codes 259
9.3 Single-Burst-Error-Correcting Codes 267
9.4 Interleaved Codes 277
9.5 Phased-Burst-Error-Correcting Codes 272
9.6 Burst-and-Random-Error-Correcting Codes 27 4
9.7 Modified Fire Codes for Simultaneous Correction
of Burst and Random Errors 280
Problems 282
References 284
CHAPTER 10 CONVOLUTIONAL CODES 287
10.1 Encoding of Convolutional Codes 288
10.2 Structural Properties of Convolutional Codes 295
10.3 Distance Properties of Convolutional Codes 308
Problems 312
References 313
CHAPTER 11 MAXIMUM UKEUHOOD DECODING
OF CONVOLUTIONAL CODES 315
11.1 The Viterbi Algorithm 315
11.2 Performance Bounds for Convolutional Codes 322
Contents ix
11.3 Construction of Good Convolutional Codes
11.4 Implementation of the Viterbi Algorithm
11.5 Modifications of the Viterbi Algorithm
Problems 346
References 348
329
337
345
CHAPTER 12 SEQUENTIAL DECODING OF CONVOLUTIONAL
CODES 350
12. l The Stack Algorithm 351
12.2 The Fano Algorithm 360
12.3 Performance Characteristics of Sequential Decoding 364
12.4 Code Construction for Sequential Decoding 37 4
12.5 Other Approaches to Sequential Decoding 380
Problems 384
References 386
CHAPTER 13 MAJORITY-LOGIC DECODING OF CONVOLUTIONAL
CODES 388
13.1 Feedback Decoding 389
13.2 Error Propagation and Definite Decoding 406
13.3 Distance Properties and Code Performance 408
13.4 Code Construction for Majority-Logic Decoding 414
13.5 Comparison with Probabilistic Decoding 424
Problems 426
References 428
CHAPTER 14 BURST-ERROR-CORRECTING CONVOLUTIONAL
CODES 429
14.1 Bounds on Burst-Error-Correcting Capability 430
14.2 Burst-Error-Correcting Convolutional Codes 430
14.3 Interleaved Convolutional Codes 441
14.4 Burst-and-Random-Error-Correcting Convolutional Codes 442
Problems 455
References 456
CHAPTER 15 AUTOMATIC-REPEAT-REQUEST STRATEGIES 458
X
15.1 Basic ARQ Schemes 459
15.2 Selective-Repeat ARQ System with Finite Receiver Buffer
15.3 ARQ Schemes with Mixed Modes of Retransmission
15.4 Hybrid ARQ Schemes 477
15.5 Class of Half-Rate Invertible Codes 481
465
474
Contents
15.6 Type II Hybrid Selective-Repeat ARQ
Problems 494
References 495
CHAPTER. 16 APPUCATIONS OF BLOCK CODES FOR. ERR.OR.
CONTROL IN DATA STORAGE SYSTEMS 498
16.1 Error Control for Computer Main Processor
and Control Storages 498
16.2 Error Control for Magnetic Tapes 503
16.3 Error Control in IBM 3850 Mass Storage System 516
16.4 Error Control for Magnetic Disks 525
16.5 Error Control in Other Data Storage Systems 531
Problems 532
References 532
CHAPTER. 17 PRACTICAL APPUCATIONS OF CONVOLUTIONAL
CODES 533
17.1 Applications of Viterbi Decoding 533
17.2 Applications of Sequential Decoding 539
17.3 Applications of Majority-Logic Decoding 543
17.4 Applications to Burst-Error Correction 547
17.5 Applications of Convolutional Codes in ARQ Systems 551