Decay of Correlations in Low Density Parity Check Codes: Low Noise Regime

Details Decay of Correlations in Low Density Parity Check Codes: Low Noise Regime Decay of Correlations in Low Density Parity Check Codes: Low Noise Regime

2009-01-23

arxiv.org/abs/0901.3630v1

Computer Science

Information Theory

5 pages, submitted to ISIT 2009

Scientific paper

Consider transmission over a binary additive white gaussian noise channel using a fixed low-density parity check code. We consider the posterior measure over the code bits and the corresponding correlation between two codebits, averaged over the noise realizations. We show that for low enough noise variance this average correlation decays exponentially fast with the graph distance between the code bits. One consequence of this result is that for low enough noise variance the GEXIT functions (further averaged over a standard code ensemble) of the belief propagation and optimal decoders are the same.

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