標題: On the Maximum Size of Block Codes Subject to a Distance Criterion
作者: Chang, Ling-Hua
Chen, Po-Ning
Tan, Vincent Y. F.
Wang, Carol
Han, Yunghsiang S.
電信工程研究所
Institute of Communications Engineering
關鍵字: Coding theory;minimum distance;block codes;graph theory
公開日期: 1-Jun-2019
摘要: We establish a general formula for the maximum size of finite length block codes with minimum pairwise distance no less than d. The achievability argument involves an iterative construction of a set of radius-d balls, each centered at a codeword. We demonstrate that the number of such balls that cover the entire code space cannot exceed this maximum size. Our approach can be applied to codes i) with elements over arbitrary code alphabets, and ii) under a broad class of distance measures. Our formula indicates that the maximum code size can be fully characterized by the cumulative distribution function of the distance measure evaluated at two independent and identically distributed random codewords. When the two random codewords assume a uniform distribution over the entire code alphabet, our formula recovers and thus naturally generalizes the Gilbert-Varshamov (GV) lower bound. Finally, we extend our study to the asymptotic setting.
URI: http://dx.doi.org/10.1109/TIT.2018.2889244
http://hdl.handle.net/11536/152351
ISSN: 0018-9448
DOI: 10.1109/TIT.2018.2889244
期刊: IEEE TRANSACTIONS ON INFORMATION THEORY
Volume: 65
Issue: 6
起始頁: 3751
結束頁: 3757
Appears in Collections:Articles