On Optimal Finite-length Binary Codes of Four Codewords for Binary Symmetric Channels

DOI

抄録

Finite-length binary codes of four codewords are studied for memoryless binary symmetric channels (BSCs) with the maximum likelihood decoding. For any block-length, best linear codes of four codewords have been explicitly characterized, but whether linear codes are better than nonlinear codes or not is unknown in general. In this paper, we show that for any block-length, there exists an optimal code of four codewords that is either linear or in a subset of nonlinear codes, called Class-I codes. Based on the analysis of Class-I codes, we derive sufficient conditions such that linear codes are optimal. For block-length less than or equal to 8, our analytical results show that linear codes are optimal. For block-length up to 300, numerical evaluations show that linear codes are optimal.

収録刊行物

  • IEICE Proceeding Series

    IEICE Proceeding Series 65 146-150, 2020-10-18

    The Institute of Electronics, Information and Communication Engineers

キーワード

詳細情報 詳細情報について

  • CRID
    1390569148830202112
  • NII論文ID
    230000012632
  • DOI
    10.34385/proc.65.b01-5
  • ISSN
    21885079
  • 本文言語コード
    en
  • データソース種別
    • JaLC
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用不可

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