Tightened Upper Bounds on the ML Decoding Error Probability of Binary Linear Block Codes

TL;DR

This paper derives tighter upper bounds on the ML decoding error probability for binary linear block codes, applicable to various channels and code ensembles, improving the accuracy of performance predictions.

Contribution

It introduces new, tightened upper bounds on decoding error probabilities that are valid for any memoryless, binary-input, output-symmetric channel, with enhancements via spectrum expurgation.

Findings

Tighter upper bounds improve error probability estimates.

Bounds are applicable to turbo-like code ensembles over AWGN.

Expurgation further refines the bounds.

Abstract

The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid for any memoryless, binary-input and output-symmetric communication channel, and their effectiveness is exemplified for various ensembles of turbo-like codes over the AWGN channel. An expurgation of the distance spectrum of binary linear block codes further tightens the resulting upper bounds.