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.
General
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