標題: Nonlinear Codes Outperform the Best Linear Codes on the Binary Erasure Channel
作者: Chen, Po-Ning
Lin, Hsuan-Yin
Moser, Stefan M.
電機學院
College of Electrical and Computer Engineering
關鍵字: Binary erasure channel;generalized Plotkin bound;optimal nonlinear channel coding;r-wise Hamming distance;weak flip codes
公開日期: 2015
摘要: The exact value of the average error probability of an arbitrary code (linear or nonlinear) using maximum likelihood decoding is studied on binary erasure channels (BECs) with arbitrary erasure probability 0 < delta < 1. The family of the fair linear codes, which are equivalent to a concatenation of several Hadamard linear codes, is proven to perform better (in the sense of average error probability with respect to maximum-likelihood decoding) than all other linear codes for many values of the blocklength n and for a dimension k = 3. It is then noted that the family of fair linear codes and the family of fair nonlinear weak fit\'\', codes both maximize the minimum Hamming distance under certain blocklengths. However, the fair nonlinear weak flip codes actually outperform the fair linear codes, i.e., linearity and global optimality cannot be simultaneously achieved for the number of codewords being M - 2(3).
URI: http://hdl.handle.net/11536/136303
ISBN: 978-1-4673-7704-1
期刊: 2015 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT)
起始頁: 1751
結束頁: 1755
Appears in Collections:Conferences Paper