Partial ordering of error patterns for maximum likelihood soft decoding

Abstract

The error patterns, encountered in maximum likelihood soft decision syndrome decoding of a binary linear block code, can be partially ordered in a way that only the minimal elements have to be scored. The ordering requires a usually short sorting proceedure applied to the confidence values of the hard-detected bits. In this paper some properties of the minimal elements are derived. We also present bounds on the number of minimal elements with particularly large Hamming weight.