Optimal ultrasmall block-codes for binary discrete memoryless channels

Po-Ning Chen, Hsuan Yin Lin, Stefan M. Moser

研究成果: Article同行評審

21 引文 斯高帕斯(Scopus)

摘要

Optimal block-codes (in the sense of minimum average error probability, using maximum likelihood decoding) with a small number of codewords are investigated for the binary asymmetric channel (BAC), including the two special cases of the binary symmetric channel (BSC) and the Z-channel (ZC), both with arbitrary cross-over probabilities. For the ZC, the optimal code structure for an arbitrary finite blocklength is derived in the cases of two, three, and four codewords and conjectured in the case of five codewords. For the BSC, the optimal code structure for an arbitrary finite blocklength is derived in the cases of two and three codewords and conjectured in the case of four codewords. For a general BAC, the best codebooks under the assumption of a threshold decoder are derived for the case of two codewords. The derivation of these optimal codes relies on a new approach of constructing and analyzing the codebook matrix not rowwise (codewords), but columnwise. This new tool leads to an elegant definition of interesting code families that is recursive in the blocklength n and admits their exact analysis of error performance. This allows for a comparison of the average error probability between all possible codebooks.

原文English
文章編號6576303
頁(從 - 到)7346-7378
頁數33
期刊IEEE Transactions on Information Theory
59
發行號11
DOIs
出版狀態Published - 4 11月 2013

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