On Optimal Finite-length Binary Codes of Four Codewords for Binary Symmetric Channels
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- Yanyan Dong
- The Chinese University of Hong Kong, Shenzhen
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- Shenghao Yang
- The Chinese University of Hong Kong, Shenzhen
Abstract
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.
Journal
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- IEICE Proceeding Series
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IEICE Proceeding Series 65 146-150, 2020-10-18
The Institute of Electronics, Information and Communication Engineers
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Details 詳細情報について
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- CRID
- 1390569148830202112
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- NII Article ID
- 230000012632
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- ISSN
- 21885079
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- Text Lang
- en
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- Data Source
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- JaLC
- CiNii Articles
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- Abstract License Flag
- Disallowed