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# Woven convolutional graph codes with large free distances

Problems of Information Transmission (Impact Factor: 0.3). 01/2011; 47(1):1-14. DOI: 10.1134/S0032946011010017

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**ABSTRACT:**Encoders for convolutional codes with large free distances can be constructed by combining several less powerful convolutional encoders. This paper is devoted to constructions in which the constituent convolutional codes are woven together in a manner that resembles the structure of a fabric. The general construction is called twill and it is described together with two special cases, viz., woven convolutional encoders with outer warp and with inner warp. The woven convolutional encoders inherit many of their structural properties, such as minimality and catastrophicity, from their constituent encoders. For all three types of woven convolutional codes upper and lower bounds on their free distances as well as lower bounds on the active distances of their encoders are derivedIEEE Transactions on Information Theory 02/2002; · 2.62 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A construction of woven graph codes based on constituent convolutional codes is studied. It is shown that within the random ensemble of such codes there exist asymptotically good codes with short fixed constituent codes. An example of a rate R = 1/3 woven graph code with free distance equal to 32 based on rate R c = 2/3 constituent convolutional codes with overall constraint length 5 is given.Information Theory, 2007. ISIT 2007. IEEE International Symposium on; 07/2007 - [Show abstract] [Hide abstract]

**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 Â¿c=5, is given.IEEE Transactions on Information Theory 01/2010; 56(1):121-129. · 2.62 Impact Factor

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