An Efficient Maximum-Likelihood Decoding Algorithm using Generator Matrix for Error Correcting Block Codes

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  • 生成行列を用いた誤り訂正符号の効率的最尤復号法
  • セイセイ ギョウレツ オ モチイタ アヤマリ テイセイ フゴウ ノ コウリツテキ サイユウフクゴウホウ

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Maximum-Likelihood Decoding (MLD) is the most powerful decoding for error correcting codes to minimize the decoding error probability. However, the complexity of MLD for linear block codes is very large. Therefore, many researchers have been investigating to reduce the time and space complexity of MLD. D. Gazelle and J. Snyders have proposed an efficient MLD method using reliability-based code-search algorithm. This decoding algorithm consecutively generates candidate codewords of maximum likelihood one. Then this algorithm reduces the complexity of MLD by eliminating unnecessary candidate codewords effectively. We propose an algorithm that efficiently generates the next candidate codeword by storing previously generated codewords for Gazelle et al. MLD decoding. Furthermore, we propose a new method to calculate the metrics of several candidate codewords at once. Finally, we show that the complexity of the proposed decoding method is reduced compared to Gazelle et al. decoding without increase of decoding error probability.

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