標題: Optimal Ultrasmall Block-Codes for Binary Discrete Memoryless Channels
作者: Chen, Po-Ning
Lin, Hsuan-Yin
Moser, Stefan M.
電機資訊學士班
Undergraduate Honors Program of Electrical Engineering and Computer Science
關鍵字: Binary asymmetric channel (BAC);binary symmetric channel (BSC);finite blocklength;flip codes;maximum likelihood (ML) decoder;minimum average error probability;optimal codes;weak flip codes;Z-channel (ZC)
公開日期: 1-Nov-2013
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 and admits their exact analysis of error performance. This allows for a comparison of the average error probability between all possible codebooks.
URI: http://dx.doi.org/10.1109/TIT.2013.2276893
http://hdl.handle.net/11536/22951
ISSN: 0018-9448
DOI: 10.1109/TIT.2013.2276893
期刊: IEEE TRANSACTIONS ON INFORMATION THEORY
Volume: 59
Issue: 11
起始頁: 7346
結束頁: 7378
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