Computer Science – Information Theory
Scientific paper
2009-11-23
IEEE Transactions on Information Theory, Vol. 57, No. 2, February 2011
Computer Science
Information Theory
Published in the Ralf Koetter Memorial Issue of IEEE Transactions on Information Theory
Scientific paper
10.1109/TIT.2010.2094812
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum distance of codes in these ensembles grows linearly with the code length. We show that these codes can correct a linearly growing number of errors under simple iterative decoding algorithms. In particular, we show that this property extends to codes constructed by parallel concatenation of Hamming codes and other codes with small minimum distance. Previously known results that proved this property for graph codes relied on graph expansion and required the choice of local codes with large distance relative to their length.
Barg Alexander
Mazumdar Arya
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