Distance Spectrum Formula For The Largest Minimum Hamming Distance Of Finite-Length Binary Block Codes
2017 IEEE INFORMATION THEORY WORKSHOP (ITW)(2017)
摘要
In this paper, an exact distance spectrum formula for the largest minimum Hamming distance of finite-length binary block codes is presented. The exact formula indicates that the largest minimum distance of finite-length block codes can be fully characterized by the information spectrum of the Hamming distance between two independent and identically distributed (i.i.d.) random codewords. The distance property of finite-length block codes is then connected to the distance spectrum. A side result of this work is a new lower bound to the largest minimum distance of finite-length block codes. Numerical examinations show that the new lower bound improves the finite-length Gilbert-Varshamov lower bound and can reach the minimum distance of existing finite-length block codes.
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关键词
largest minimum hamming distance,finite-length binary block codes,exact distance spectrum formula,largest minimum distance,finite-length block codes,distance property,finite-length Gilbert-Varshamov
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