Weak flip codes and applications to optimal code design on the binary erasure channel

Po-Ning Chen*, Hsuan Yin Lin, Stefan M. Moser

*此作品的通信作者

研究成果: Conference contribution同行評審

6 引文 斯高帕斯(Scopus)

摘要

A new family of nonlinear codes, called weak flip codes, is presented and is shown to contain many beautiful properties. In particular, the subfamily of fair weak flip codes can be seen as a generalization of linear codes. Different from linear codes that only exist for a number of codewords M being an integer-power of 2, the fair weak flip code can be defined for an arbitrary M. It is then noted that the fair weak flip codes are related to binary nonlinear Hadamard codes: both code families maximize the minimum Hamming distance and meet the Plotkin bound. However, while the binary nonlinear Hadamard codes have only been shown to possess good Hamming-distance properties, the fair weak flip codes are proven to be globally optimal (in the sense of minimizing the error probability) among all linear or nonlinear codes for the binary erasure channel (BEC) for many values of the blocklength n and for M≤6. For M>6, similar optimality results are conjectured. The results in this paper are founded on a new powerful tool for the analysis and generation of block codes: the column-wise approach to the codebook matrix.

原文English
主出版物標題2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
頁面160-167
頁數8
DOIs
出版狀態Published - 1 12月 2012
事件2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012 - Monticello, IL, United States
持續時間: 1 10月 20125 10月 2012

出版系列

名字2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012

Conference

Conference2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
國家/地區United States
城市Monticello, IL
期間1/10/125/10/12

指紋

深入研究「Weak flip codes and applications to optimal code design on the binary erasure channel」主題。共同形成了獨特的指紋。

引用此