Complete Enumeration of Stopping Sets of Full-Rank Parity-Check Matrices of Hamming Codes

Details Complete Enumeration of Stopping Sets of Full-Rank Parity-Check Matrices of Hamming Codes Complete Enumeration of Stopping Sets of Full-Rank Parity-Check Matrices of Hamming Codes

2006-03-02

arxiv.org/abs/cs/0603007v1

Computer Science

Information Theory

7 pages, submitted to the IEEE Transactions on Information Theory

Scientific paper

Stopping sets, and in particular their numbers and sizes, play an important role in determining the performance of iterative decoders of linear codes over binary erasure channels. In the 2004 Shannon Lecture, McEliece 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 correspondence, we derive an expression for the number of stopping sets of any given size for the same parity-check matrix.

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