Searching for Voltage Graph-Based LDPC Tailbiting Codes with Large Girth

Abstract

The relation between parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Using the principle of tailbiting, compact representations of bipartite graphs based on convolutional codes can be found. Bounds on the girth and the minimum distance of LDPC block codes constructed in such a way are discussed. Algorithms for searching iteratively for LDPC block codes with large girth and for determining their minimum distance are presented. Constructions based on all-ones matrices, Steiner Triple Systems, and QC block codes are introduced. Finally, new QC regular LDPC block codes with girth up to 24 are given.

Submitted to IEEE Transactions on Information Theory in February 2011

References in corpus (2)

• Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform so well over the BEC
• Girth-12 Quasi-Cyclic LDPC Codes with Consecutive Lengths

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• Integer Ring Sieve for Constructing Compact QC-LDPC Codes with Girths 8, 10, and 12
• On the lifting degree of girth-8 QC-LDPC codes
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