Enumeration of stopping sets of full-rank parity-check matrices of hammng codes

Conference paper (2006)

Authors

KAS Abdel-Ghaffar External organisation
J.H. Weber Wireless and Mobile Communications
Research Group
Wireless and Mobile Communications
More Info
expand_more

Published Date

2006

Language

Undefined/Unknown

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Research Group

Wireless and Mobile Communications

Abstract

Iterative techniques have been proposed for decoding linear binary block codes over erasure channels. The performance of such decoding techniques depends on the parity-check matrices used, and in partivular, on the numbers and sizes of stopping sets of these matrices. In the 2004 Shannon lecture, McElliece presented an expression for the number of stopping sets of size three for a full-rank parity-check matrix of the Hamming code. In this paper, we present an expression for the number of stopping sets of any given size for the same parity-check matrix.