標題: Equidistant Codes Meeting the Plotkin Bound are Not Optimal on the Binary Symmetric Channel
作者: Chen, Po-Ning
Lin, Hsuan-Yin
Moser, Stefan M.
電機資訊學士班
Undergraduate Honors Program of Electrical Engineering and Computer Science
公開日期: 1-一月-2013
摘要: In this paper, we re-introduce from our previous work [1] a new family of nonlinear codes, called weak flip codes, and show that its subfamily fair weak flip codes belongs to the class of equidistant codes, satisfying that any two distinct codewords have identical Hamming distance. It is then noted that the fair weak flip codes are related to the binary nonlinear Hadamard codes as both code families maximize the minimum Hamming distance and meet the Plotkin upper bound under certain blocklengths. Although the fair weak flip codes have the largest minimum Hamming distance and achieve the Plotkin bound, we find that these codes are by no means optimal in the sense of average error probability over binary symmetric channels (BSC). In parallel, this result implies that the equidistant Hadamard codes are also nonoptimal over BSCs. Such finding is in contrast to the conventional code design that aims at the maximization of the minimum Hamming distance. The results in this paper are proved by examining the exact error probabilities of these codes on BSCs, using the column-wise analysis on the codebook matrix.
URI: http://hdl.handle.net/11536/125032
ISBN: 978-1-4799-0446-4
ISSN: 
期刊: 2013 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT)
起始頁: 3015
結束頁: 3019
顯示於類別:會議論文