Coding Techniques for Linear Block Codes With Applications to Fault Identification

Abstract

131 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.When channel reliability information is available, soft-decision decoding becomes attractive for many applications, since maximum-likelihood (ML) soft-decision decoding offers (roughly) 3 dB additional gain over algebraic decoding. Since ML soft-decision decoding is an NP-hard problem, we concentrate our efforts on exploring computationally efficient suboptimal soft-decision decoding methods, based on iterative recoding, a methodology that attempts to systematically search through reliable information (basis) bits while applying recoding to correct errors among the remaining unreliable redundancy bits. We first determine the optimal ordering of test error patterns when given an information basis, and then characterize the optimality of the so-called most reliable basis. We next develop two techniques, namely preprocessing and diversification, which significantly improve the traditional iterative recoding method. We also carry out analysis of the asymptotic behavior of the proposed decoding algorithm under the AWGN channel model in the high SNR regime. As a by-product of this analysis, we also precisely characterize the asymptotic behavior of the state-of-the-art Chase and GMD decoding algorithms for the AWGN channel model.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD