Beyond the Bethe Free Energy of LDPC Codes via Polymer Expansions

The loop series provides a formal way to write down corrections to the Bethe entropy (and/or free energy) of graphical models. We provide methods to rigorously control such expansions for low-density parity-check codes used over a highly noisy binary symmetric channel. We prove that in the asymptotic limit of large size, with high probability, the Bethe expression gives an exact formula for the entropy (per bit) of the input word conditioned on the output of the channel. Our methods also apply to more general models.


Published in:
2012 Ieee International Symposium On Information Theory Proceedings (Isit)
Presented at:
IEEE International Symposium on Information Theory
Year:
2012
Publisher:
New York, Ieee
ISBN:
978-1-4673-2579-0
Laboratories:




 Record created 2013-03-28, last modified 2018-03-17


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