Summary

The 2018 International Symposium on Information Theory and Its Applications (ISITA2018)

2018

Session Number:Mo-PM-1-2

Session:

Number:Mo-PM-1-2.4

Connections Between the Error Probability and the r-wise Hamming Distances

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

pp.130-134

Publication Date:2018/10/18

Online ISSN:2188-5079

DOI:10.34385/proc.55.Mo-PM-1-2.4

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Summary:
An extension from the pairwise Hamming distance to the r-wise Hamming distance is presented. It can be used to fully characterize the maximum-likelihood decoding (MLD) error of an arbitrary code over the binary erasure channel (BEC). By noting that good codes always have large minimum r-wise Hamming distances for all r, a new design criterion for a code is introduced: the minimum r-wise Hamming distance. We then prove an upper bound for the minimum r-wise Hamming distance of an arbitrary code, called the generalized Plotkin bound, and provide a class of (nonlinear) codes that achieve the bound for every r.