TY - GEN

T1 - Connections between the Error Probability and the r-wise Hamming Distances

AU - Lin, Hsuan Yin

AU - Moser, Stefan Michael

AU - Chen, Po-Ning

PY - 2019/3/8

Y1 - 2019/3/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85063909445&partnerID=8YFLogxK

U2 - 10.23919/ISITA.2018.8664296

DO - 10.23919/ISITA.2018.8664296

M3 - Conference contribution

AN - SCOPUS:85063909445

T3 - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

SP - 130

EP - 134

BT - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 15th International Symposium on Information Theory and Its Applications, ISITA 2018

Y2 - 28 October 2018 through 31 October 2018

ER -