Information Theory Gallager bounds on the performance of maximum-likelihood decoded linear binary block codes in AWGN interference

Performance evaluation of maximum-likelihood (ML) soft-decision-decoded binary block codes is usually carried out using bounding techniques. Many tight upper bounds on the error probability of binary codes are based on the so-called Gallager's first bounding technique (GFBT). In this method, Gallager bisects the error probability to the joint probability of error and noise residing in a region ℜ (here referred to as the Gallager region) plus joint probability of error and noise residing in the complement of ℜ (also referred to as regions of many and few errors, respectively); where ℜ is a volume around the transmitted codeword. In this tutorial review, a comprehensive study of a number of upper bounds on the error probability of ML decoding of binary codes based on GFBT is provided. For some bounds, their applicability to other schemes is also pointed out and argued. We also provide an overview of bounds based on Gallager's second bounding technique (GSBT) and discuss some of their relations and interconnections. Copyright © 2006 AEIT

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