Graph Configurations and Decoding Performance
Proceedings of the 8th IMA International Conference on Cryptography and Coding
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IEEE Transactions on Information Theory
On universal properties of capacity-approaching LDPC code ensembles
IEEE Transactions on Information Theory
On the fundamental system of cycles in the bipartite graphs of LDPC code ensembles
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
On the hardness of approximating stopping and trapping sets
IEEE Transactions on Information Theory
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IEEE Transactions on Information Theory - Special issue on information theory in molecular biology and neuroscience
Codes with girth 8 Tanner graph representation
Designs, Codes and Cryptography
IEEE Transactions on Information Theory
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If a linear block code C of length n has a Tanner graph without cycles, then maximum-likelihood soft-decision decoding of C can be achieved in time O(n2). However, we show that cycle-free Tanner graphs cannot support good codes. Specifically, let C be an (n,k,d) linear code of rate R=k/n that can be represented by a Tanner graph without cycles. We prove that if R⩾0.5 then d⩽2, while if R<0.5 then C is obtained from a code of rate ⩾0.5 and distance ⩽2 by simply repeating certain symbols. In the latter case, we prove that d⩽[n/k+1]+[n+1/k+1]<2/R. Furthermore, we show by means of an explicit construction that this bound is tight for all values of n and k. We also prove that binary codes which have cycle-free Tanner graphs belong to the class of graph-theoretic codes, known as cut-set codes of a graph. Finally, we discuss the asymptotics for Tanner graphs with cycles, and present a number of open problems for future research