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

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 G EXIT functions (further averaged over a standard code ensemble) of the belief propagation and optimal decoders are the same.

Published in:
2009 Ieee International Symposium On Information Theory, Vols 1- 4, 2654-2658
Presented at:
IEEE International Symposium on Information Theory (ISIT 2009), Seoul, SOUTH KOREA, Jun 28-Jul 03, 2009
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa

 Record created 2010-11-30, last modified 2018-03-17

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