DocumentCode :
3511787
Title :
Linear growing minimum distance of ultra-sparse non-binary cluster-LDPC codes
Author :
Savin, Valentin ; Declercq, David
Author_Institution :
LETI, CEA, Grenoble, France
fYear :
2011
fDate :
July 31 2011-Aug. 5 2011
Firstpage :
523
Lastpage :
527
Abstract :
In this paper, we study the asymptotic minimum distance of non-binary cluster-LDPC codes whose subjacent binary parity-check matrix is composed of localized density of ones, concentrated in clusters of bits. A particular attention is given to cluster codes represented by ultra-sparse bipartite graphs, in the sense that each symbol-node is connected to exactly dv = 2 constraint-nodes. We derive a lower bound on the minimum distance of non-binary cluster-LDPC codes and we show that there exist ensembles of ultra-sparse codes whose minimum distance grows linearly with the code length (with probability going to 1 as the code length goes to infinity). This result is in contrast with “classical” non-binary LDPC codes based on graphs with strictly regular dv = 2 symbol-nodes, whose minimum distance grows at most logarithmically with the code length. We also show that one can build practical non-binary cluster-LDPC codes with various finite codeword lengths, whose minimum distance is close to the Gilbert-Varshamov bound.
Keywords :
graph theory; parity check codes; Gilbert-Varshamov bound; finite codeword lengths; linear growing minimum distance; subjacent binary parity-check matrix; ultrasparse bipartite graphs; ultrasparse nonbinary cluster-LDPC codes; Algorithm design and analysis; Bipartite graph; Eigenvalues and eigenfunctions; Joining processes; Parity check codes; Sparse matrices; Symmetric matrices; Gilbert-Varshamov bound; Non-binary cluster-LDPC codes; graph codes; minimum distance;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on
Conference_Location :
St. Petersburg
ISSN :
2157-8095
Print_ISBN :
978-1-4577-0596-0
Electronic_ISBN :
2157-8095
Type :
conf
DOI :
10.1109/ISIT.2011.6034183
Filename :
6034183
Link To Document :
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