Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial (Foundations and Trends in Communications and Information Theory)

✍ Scribed by Igal Sason, Shlomo Shamai

• Year: 2006
• Tongue: English
• Leaves: 237
• Category: Library

✦ Synopsis

Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial focuses on the performance evaluation of linear codes under optimal maximum-likelihood (ML) decoding. Though the ML decoding algorithm is prohibitively complex for most practical codes, their performance analysis under ML decoding allows to predict their performance without resorting to computer simulations. Performance Analysis of Linear Codes under Maximum-Likelihood Decoding: A Tutorial is a comprehensive introduction to this important topic for students, practitioners and researchers working in communications and information theory.

✦ Table of Contents

Introduction......Page 12
General approach for the derivation of improved upper bounds......Page 14
On Gallager bounds: Variations and applications......Page 17
Lower bounds on the decoding error probability......Page 19
Union bounds......Page 24
Union bounds for turbo-like codes......Page 28
The methodology of the bounding technique......Page 32
Improved upper bounds for the Gaussian channel......Page 34
Improved upper bounds for fading channels......Page 90
Concluding comments......Page 99
Introduction......Page 102
Gallager bounds for symmetric memoryless channels......Page 104
Interconnections between bounds......Page 115
Special cases of the DS2 bound......Page 121
Gallager-type bounds for the mismatched decoding regime......Page 137
Gallager-type bounds for parallel channels......Page 146
Some applications of the Gallager-type bounds......Page 147
Summary and conclusions......Page 162
Introduction......Page 166
The 1959 Shannon lower bound for the AWGN channel......Page 168
The 1967 sphere-packing bound......Page 174
Sphere-packing bounds revisited for moderate block lengths......Page 187
Concluding comments......Page 191
Introduction......Page 194
Lower bounds based on de Caen's inequality and variations......Page 198
Summary and conclusions......Page 209
Concluding Remarks......Page 212
Acknowledgments......Page 218
References......Page 220