Title :
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
fDate :
4/1/2012 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2176717
