The polynomial error probability for LDPC codes

Details The polynomial error probability for LDPC codes The polynomial error probability for LDPC codes

2003-10-08

arxiv.org/abs/cond-mat/0310177v1

Physics

Condensed Matter

Statistical Mechanics

15 pages 13 figures

Scientific paper

We obtain exact expressions for the asymptotic behaviour of the average probability of the block decoding error for ensembles of regular low density parity check error correcting codes, by employing diagrammatic techniques. Furthermore, we show how imposing simple constraints on the code ensemble (that can be practically implemented in linear time), allows one to suppress the error probability for codes with more than 2 checks per bit, to an arbitrarily low power of $N$. As such we provide a practical route to a (sub-optimal){\em expurgated} ensemble.

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