Woven graph codes: asymptotic performances and examples

Authors:
Irina E. Bocharova;Rolf Johannesson;Boris D. Kudryashov;Viktor V. Zyablov
Affiliations:
Department of Information Systems, St. Petersburg University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia;Department of Information Technology, Lund University, Lund, Sweden;Department of Information Systems, St. Petersburg University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia;Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 8
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A rate R = 5/20 hypergraph-based woven convolutional code with free distance 120

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Woven convolutional graph codes with large free distances

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Abstract

Constructions of woven graph codes based on constituent block and convolutional codes are studied. It is shown that within the random ensembles of such codes based on s-partite, s-uniform hypergraphs, where s depends only on the code rate, there exist codes satisfying the Gilbert--Varshamov (GV) and the Costello lower bound on the minimum distance and the free distance, respectively. A connection between regular bipartite graphs and tailbiting (TB) codes is shown. Some examples of woven graph codes are presented. Among them, an example of a rate Rwg = 1/3 woven graph code with dfree =32 based on Heawood's bipartite graph, containing n = 7 constituent rate Rc = 2/3 convolutional codes with overall constraint lengths Vc = 5, is given.