Low-Density Parity-Check Codes Which Can Correct Three Errors Under Iterative Decoding

Details Low-Density Parity-Check Codes Which Can Correct Three Errors Under Iterative Decoding Low-Density Parity-Check Codes Which Can Correct Three Errors Under Iterative Decoding

2008-10-07

arxiv.org/abs/0810.1105v1

Computer Science

Information Theory

25 pages. 11 Figures. Part of the work was presented at the Information Theory Workshop (ITW), May 5-9 2008, Porto, Portugal.

Scientific paper

In this paper, we give necessary and sufficient conditions for low-density parity-check (LDPC) codes with column-weight three to correct three errors when decoded using hard-decision message-passing decoding. Additionally, we give necessary and sufficient conditions for column-weight-four codes to correct three errors in four iterations of hard-decision message-passing decoding. We then give a construction technique which results in codes satisfying these conditions. We also provide numerical assessment of code performance via simulation results.

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