Complexity Reduction of the Gazelle and Snyders Decoding Algorithm for Maximum Likelihood Decoding

Hideki YAGI  Manabu KOBAYASHI  Shigeichi HIRASAWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A    No.10    pp.2461-2472
Publication Date: 2003/10/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
maximum likelihood decoding,  information set decoding,  most reliable basis,  reliability measure,  linear block codes,  

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Several reliability based code search algorithms for maximum likelihood decoding have been proposed. These algorithms search the most likely codeword, using the most reliable information set where the leftmost k (the dimension of code) columns of generator matrix are the most reliable and linearly independent. Especially, D. Gazelle and J. Snyders have proposed an efficient decoding algorithm and this algorithm requires small number of candidate codewords to find out the most likely codeword. In this paper, we propose new efficient methods for both generating candidate codewords and computing metrics of candidate codewords to obtain the most likely codeword at the decoder. The candidate codewords constructed by the proposed method are identical those in the decoding algorithm of Gazelle et al. Consequently, the proposed decoding algorithm reduces the time complexity in total, compared to the decoding algorithm of Gazelle et al. without the degradation in error performance.