Concentration inequalities have been the subject of exciting developments during the last two decades, and have been intensively studied and used as a powerful tool in various areas. These include convex geometry, functional analysis, statistical physics, mathematical statistics, pure and applied probability theory, information theory, theoretical computer science, learning theory, and dynamical systems. This book focuses on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding. In addition to being a survey, it also includes various new recent results derived by the authors.This third edition of the bestselling book introduces the reader to the martingale method and the Efron-Stein-Steele inequalities in completely new sections. A new application of lossless source coding with side information is described in detail. Finally, the references have been updated and ones included that have been published since the original publication. Concentration of Measure Inequalities in Information Theory, Communications, and Coding is essential reading for all researchers and scientists in information theory and coding.

This second edition includes several new sections and provides a full update on all sections. This book was welcomed when it was first published as an important comprehensive treatment of the subject which is now brought fully up to date. Concentration inequalities have been the subject of exciting developments during the last two decades, and have been intensively studied and used as a powerful tool in various areas. These include convex geometry, functional analysis, statistical physics, mathematical statistics, pure and applied probability theory (e.g., concentration of measure phenomena in random graphs, random matrices, and percolation), information theory, theoretical computer science, learning theory, and dynamical systems. Concentration of Measure Inequalities in Information Theory, Communications, and Coding focuses on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding. In addition to being a survey, this monograph also includes various new recent results derived by the authors. It is essential reading for all researchers and scientists in information theory and coding.

This book 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. It also provides a benchmark for testing the sub-optimality of iterative (or other practical) decoding algorithms. This analysis also establishes the goodness of linear codes (or ensembles), determined by the gap between their achievable rates under optimal ML decoding and information theoretical limits. In this book, upper and lower bounds on the error probability of linear codes under ML decoding are surveyed and applied to codes and ensembles of codes on graphs. For upper bounds, the authors discuss various bounds where focus is put on Gallager bounding techniques and their relation to a variety of other reported bounds. Within the class of lower bounds, they address de Caen's based bounds and their improvements, and also consider sphere-packing bounds with their recent improvements targeting codes of moderate block lengths. Performance Analysis of Linear Codes under Maximum-Likelihood Decoding is a comprehensive introduction to this important topic for students, practitioners and researchers working in communications and information theory.