Optimal ultrasmall block-codes for binary discrete memoryless channels

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

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

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.

Original languageEnglish
Article number6576303
Pages (from-to)7346-7378
Number of pages33
JournalIEEE Transactions on Information Theory
Volume59
Issue number11
DOIs
StatePublished - 4 Nov 2013

Keywords

  • Binary asymmetric channel (BAC)
  • Z-channel (ZC)
  • binary symmetric channel (BSC)
  • finite blocklength
  • flip codes
  • maximum likelihood (ML) decoder
  • minimum average error probability
  • optimal codes
  • weak flip codes

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