LDPC Block and Convolutional Codes Based on Circulant Matrices

Tanner, Michael R and Sridhara, Deepak and Sridharan, Arvind and Fuja, Thomas E and Costello, Daniel J (2004) LDPC Block and Convolutional Codes Based on Circulant Matrices. In: IEEE Transactions on Information Theory, 50 (12). pp. 2966-2984.

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Abstract

A class of algebraically structured quasi-cyclic (QC) low-density parity-check (LDPC) codes and their convolutional counterparts is presented. The QC codes are described by sparse parity-check matrices comprised of blocks of circulant matrices. The sparse parity-check representation allows for practical graph-based iterative message-passing decoding. Based on the algebraic structure, bounds on the girth and minimum distance of the codes are found, and several possible encoding techniques are described. The performance of the QC LDPC block codes compares favorably with that of randomly constructed LDPC codes for short to moderate block lengths. The performance of the LDPC convolutional codes is superior to that of the QC codes on which they are based; this performance is the limiting performance obtained by increasing the circulant size of the base QC code. Finally, a continuous decoding procedure for the LDPC convolutional codes is described.

Item Type:	Journal Article
Publication:	IEEE Transactions on Information Theory
Publisher:	IEEE
Additional Information:	©2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords:	Circulant matrices;iterative decoding;low-density parity-check (LDPC) block codes;LDPC convolutional codes;LDPC codes;message-passing;quasi-cyclic (QC) codes
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	22 Feb 2008
Last Modified:	19 Sep 2010 04:42
URI:	http://eprints.iisc.ac.in/id/eprint/12910

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