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Abstract: We are interested in a function f(p) that represents the probability that a random subset of edges of a \Delta-regular graph G contains half the edges of some cycle of G. f(p) is also the probability that a codeword be corrupted beyond recognition when words of the cycle code of G are submitted to the binary symmetric channel. We derive a precise upperbound on the largest p for which f(p) can vanish when the number of edges of G goes to infinity. To this end we introduce the notion of... (Update)
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BibTeX entry: (Update)
L. Decreusefond and G. Z' emor, "On the error-correcting capabilities of cycle codes of graphs," Combinatorics, Probability, and Computing, vol. 6 (1997), pp. 27--38. http://citeseer.ist.psu.edu/decreusefond97errorcorrecting.html More
@article{ decreusefond97errorcorrecting,
author = "L. Decreusefond and G. Z\'emor",
title = "the error-correcting capabilities of cycle codes of graphs",
journal = "Combinatorics, Probability, and Computing",
volume = "6",
pages = "27--38",
year = "1997",
url = "citeseer.ist.psu.edu/decreusefond97errorcorrecting.html" }
Citations (may not include all citations):67 Random walks and percolation on trees (context) - Lyons - 1990
54 Graphes et hypergraphes (context) - Berge - 1970
27 Probabilistic characteristics of graphs with large connectiv.. (context) - Margulis - 1974
7 Graph theoretic error-correcting codes (context) - Hakimi, Bredeson - 1968
7 temps discret (context) - Neveu - 1972
3 Optimal cycle codes constructed from Ramanujan graphs (context) - Tillich, mor
2 Tome II (context) - Dellacherie, Meyer et al. - 1980
1 Threshold eoeects in codes (context) - mor - 1994
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