Title: Minimum distance and pseudodistance lower bounds for generalised LDPC codes

Authors: Christine A. Kelley

Addresses: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, USA

Abstract: Two different ways of obtaining generalised low-density parity-check (LDPC) codes are considered. Lower bounds on the minimum distance, stopping distance and pseudodistance are derived for these codes using graph-based analysis. These bounds are generalisations of Tanner|s bit- and parity-oriented bound for simple (LDPC) codes. The new bounds are useful in predicting the performance of generalised LDPC codes under maximum-likelihood decoding, graph-based iterative decoding and linear programming decoding, and rely on the connectivity of the Tanner graph.

Keywords: low-density parity check codes; LDPC codes; generalised LDPC codes; Tanner graph; bit-oriented bound; parity-oriented bound; constraint-oriented bound; iterative decoding; code graph; eigenvalues; minimum distance; stopping set; pseudoweight; minimum distance; pseudodistance; stopping distance; linear programming decoding; lower bounds.

DOI: 10.1504/IJICOT.2010.032546

International Journal of Information and Coding Theory, 2010 Vol.1 No.3, pp.313 - 333

Published online: 06 Apr 2010 *

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