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International Conference on Advanced Communication Technology

Half-Chase Algorithm of Non-soft Decision Decoding Based on Majority

Chun-Fong Kuo, Hsin-Kun Lai, Erl‐Huei Lu

Published Feb 1, 2007• 0 citations
Publisher

Abstract

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.

DOI
10.1109/icact.2007.358432

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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.
Anon-soft decision decoding algorithm forbinary linear block codes transmitted overAWGN channel ispresented. Unlike soft decision decoding algorithms, theproposed algorithm doesnotcomputing weighted Hammingdistances. Basedonthe majority ofcodewordcandidates fromtheharddecision decodingoutput,the proposedalgorithmimproves error-correcting performance byldBofcoding gaincompared tothatofharddecision decoding algorithms. Also, aschematic block diagram forfinding thecodewordofmajority isdeveloped. Furthermore, a comparison ofhardware complexity ismade between thecomputation ofweighted Hammingdistances and thefinding ofmajority codeword.
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.
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.
For the decoding of a binary block code of Hamming distance of d over AWGN channels, a soft-decision decoder is said to achieve bounded-distance (BD) decoding if its squared error-correction radius is equal to d. A Chase-3-like algorithm outputs the best (most likely) codeword in a list of candidates generated by a conventional algebraic binary decoder whose input sequences have nonzero entries confined in the most unreliable positions. Let ¿(d) denote the smallest size of input sequence sets of Chase-3-like algorithms which achieve BD decoding. In this paper, we show that there are positive numbers C1and C2such that C1¿ ¿(d)d-1/2¿ C2for sufficiently large d.