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International Conference on Innovative Computing, Information and Control

Semi-soft Decision Decoding Based on Correspondence between Error Patterns and the Relative Test Patterns

Hsin-Kun Lai, Erl‐Huei Lu

Published Sep 1, 2007• 0 citations
Publisher

Abstract

A semi-soft decision decoding algorithm based on the correspondence between error patterns and the relative test patterns for binary linear block codes over AWGN channel is presented. The proposed algorithm improves coding gain by 0.8 dB without computing weighted Hamming distances.
DOI
10.1109/icicic.2007.515

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A non-soft decision decoding algorithm for binary linear block codes transmitted over AWGN channel is presented. Unlike soft decision decoding algorithms, the proposed algorithm does not computing weighted Hamming distances. Based on the majority of code word candidates from the hard decision decoding output, the proposed algorithm improves error-correcting performance by 1 dB of coding gain compared to that of hard decision decoding algorithms. Also, a schematic block diagram for finding the codeword of majority is developed. Furthermore, a comparison of hardware complexity is made between the computation of weighted Hamming distances and the finding of majority code word.
In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received word and to present the obtained real vector r as inputs of a SIHO decoder (Soft In/Hard Out). The goal of the latter is to try to find the closest codeword to r in terms of the Euclidean distance. A comparison of the proposed algorithm over the AWGN channel with the Majority logic decoder, Berlekamp-Massey, Bit Flipping, Hartman-Rudolf algorithms and others show that it is more efficient in terms of performance. The complexity of the proposed decoder depends on the weight of the error to decode, on the code structure and also on the used SIHO decoder.
This correspondence investigates soft-decision decoding of binary linear block codes using ordered recodings of test error patterns on the so-called "most reliable basis." The analysis demonstrates the optimality of the most reliable basis by showing that, among all possible bases, the most reliable basis minimizes the list error probability for a very general (and well-defined) class of orderings for recoding operations. The correspondence then proposes a suboptimal algorithm which utilizes reprocessing ordering and incorporates two techniques that render it computationally very efficient: 1) an iterative reference recoding technique which simplifies the recoding operation required for each test error pattern, and 2) an adaptive skipping rule which significantly reduces the average number of recodings. Simulation results with codes of relatively large length show that the proposed algorithm is computationally very efficient in comparison to existing algorithms in the literature
For iterative soft-decision decoding algorithms for binary linear block codes, error performance and computational complexity are very important factors.In this thesis, suÆcient conditions of the optimality of decoded codeword and a suÆcient condition which is used for ruling-out some useless iterations of bounded distance decoding which reduces the computational complexity of iterative soft-decision decoding algorithms are shown.New iterative soft-decision decoding algorithms which uses the suÆcient conditions of the optimality of decoded codeword to achievegood error performance with small computational complexity are also shown.First, the suÆcient conditions are derived based on: (1) partial knowledge of the distance pro le of the code, and (2) previously generated candidate codewords.When the numberof previously generated candidate codewords is greater than 1, the conditions presented here are less stringent than those derived by Taipale and Pursley [4] and Kaneko et.al.[5].The condition based on three previously generated candidate codewords is the rst such s u Æ c i e n t condition that has ever been derived.It is shown by computer simulation that these suÆcient condions reduce the computational complexity of iterative decoding algorithms without degradation of error performance.Second, a suÆcient condition to rule-out some useless test error patterns is derived.In an iterative decoding algorithm, such as Chase Type-II decoding algorithm[2] and its improved versions, candidate codewords for a received vector are generated
Soft decision decoding of binary linear block codes transmitted over the additive white Gaussian channel (AWGN) using antipodal signaling is considered. A set of decoding algorithms called generalized Chase algorithms is proposed. In contrast to Chase algorithms, which require a\lfloor (d- 1)/2 \rfloorbinary error-correcting decoder for decoding a binary linear block code of minimum distanced, the generalized Chase algorithms can use a binary decoder that can correct less than\lfloor ( d - 1)/2 \rfloorhard errors. The Chase algorithms are particular cases of the generalized Chase algorithms. The performance of all proposed algorithms is asymptotically optimum for high signal-to-noise ratio (SNR). Simulation results for the(47, 23)quadratic residue code indicate that even for low SNR the performance level of a maximum likelihood decoder can be approached by a relatively simple decoding procedure.