000100850 001__ 100850
000100850 005__ 20180317094232.0
000100850 022__ $$a0018-9448
000100850 02470 $$2ISI$$a000243953400014
000100850 02470 $$2DAR$$a9791
000100850 037__ $$aARTICLE
000100850 245__ $$aGriffiths Kelly Sherman correlation inequalities: a useful tool in the theory of error correcting codes
000100850 269__ $$a2007
000100850 260__ $$bInstitute of Electrical and Electronics Engineers$$c2007
000100850 336__ $$aJournal Articles
000100850 520__ $$aIt is shown that a correlation inequality of statistical mechanics can be applied to linear low-density parity-check codes. Thanks to this tool we prove that, under a natural assumption, the exponential growth rate of regular low-density parity-check (LDPC) codes, can be computed exactly by iterative methods, at least on the interval where it is a concave function of the relative weight of code words. Then, considering communication over a binary input additive white Gaussian noise channel with a Poisson LDPC code we prove that, under a natural assumption, part of the GEXIT curve (associated to MAP decoding) can also be computed exactly by the belief propagation algorithm. The correlation inequality yields a sharp lower bound on the GEXIT curve. We also make an extension of the interpolation techniques that have recently led to rigorous results in spin glass theory and in the SAT problem.
000100850 700__ $$0241807$$aMacris, N$$g107423
000100850 773__ $$j53$$k2$$q664-683$$tIEEE TRANSACTIONS ON INFORMATION THEORY
000100850 8564_ $$s536584$$uhttps://infoscience.epfl.ch/record/100850/files/corelationinequality2007.pdf$$yn/a$$zn/a
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000100850 909C0 $$0252058$$pLTHC$$xU10432
000100850 917Z8 $$x107423
000100850 917Z8 $$x107423
000100850 937__ $$aLTHC-ARTICLE-2007-033
000100850 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000100850 980__ $$aARTICLE