Performance Analysis of Linear Codes under ML Decoding. A Tutorial

raowy2009

书名：Performance Analysis of Linear Codes under Maximum-Likelihood Decoding： A Tutorial
作者：Igal Sason, Shlomo Shamai （曾为IEEE Trans. on Information Theory 主编）
出版：NOW Publisher Inc. 2006
长度：234页

1 A Short Overview 1

1.1 Introduction 1
1.2 General approach for the derivation of improved upper bounds 3
1.3 On Gallager bounds: Variations and applications 6
1.4 Lower bounds on the decoding error probability 9

2 Union Bounds: How Tight Can They Be? 13

2.1 Union bounds 13
2.2 Union bounds for turbo-like codes 17

3 Improved Upper Bounds for Gaussian and Fading Channels 21

3.1 The methodology of the bounding technique 21
3.2 Improved upper bounds for the Gaussian channel 23
3.3 Improved upper bounds for fading channels 79
3.4 Concluding comments 88

4 Gallager-Type Upper Bounds: Variations, Connections and Applications 91

4.1 Introduction 91
4.2 Gallager bounds for symmetric memoryless channels 93
4.3 Interconnections between bounds 104
4.4 Special cases of the DS2 bound 110
4.5 Gallager-type bounds for the mismatched decoding regime 126
4.6 Gallager-type bounds for parallel channels 135
4.7 Some applications of the Gallager-type bounds 136
4.8 Summary and conclusions 151

5 Sphere-Packing Bounds on the Decoding Error Probability 155
5.1 Introduction 155
5.2 The 1959 Shannon lower bound for the AWGN channel 157
5.3 The 1967 sphere-packing bound 163
5.4 Sphere-packing bounds revisited for moderate block lengths 176
5.5 Concluding comments 180

6 Lower Bounds Based on de Caen’s Inequality and Recent Improvements 183
6.1 Introduction 183
6.2 Lower bounds based on de Caen’s inequalityand variations 187
6.3 Summary and conclusions 198

7 Concluding Remarks 201

Acknowledgments 205

References 207

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