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

Author

Bocharova, Irina E. ; Hug, Florian ; Johannesson, Rolf ; Kudryashov, Boris D. ; Satyukov, Roman V.

Author_Institution

Dept. of Inf. Syst., St. Petersburg Univ. of Inf. Technol., St. Petersburg, Russia

Volume

58

Issue

4

fYear

2012

fDate

4/1/2012 12:00:00 AM

Firstpage

2265

Lastpage

2279

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-one matrices, Steiner Triple Systems, and QC block codes are introduced. Finally, new QC regular LDPC block codes with girth up to 24 are given.

Keywords

block codes; convolutional codes; graph theory; iterative decoding; matrix algebra; parity check codes; QC regular LDPC block code; Steiner triple system; biadjacency matrix; bipartite graph compact representation; convolutional code; iterative algorithm; large girth; minimum distance determination; parity-check matrix; quasicyclic regular low-density parity-check block code; voltage graph-based LDPC tailbiting code; Bipartite graph; Block codes; Convolutional codes; Generators; Iterative decoding; Linear matrix inequalities; Biadjacency matrix; Tanner graph; convolutional code; girth; low-density parity-check (LDPC) code; minimum distance; tailbiting;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2011.2176717

Filename

6084747