100850
20190316233935.0
0018-9448
000243953400014
ISI
9791
DAR
ARTICLE
Griffiths Kelly Sherman correlation inequalities: a useful tool in the theory of error correcting codes
2007
Institute of Electrical and Electronics Engineers
2007
Journal Articles
It 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.
Macris, N
107423
241807
664-683
2
IEEE TRANSACTIONS ON INFORMATION THEORY
53
n/a
536584
n/a
http://infoscience.epfl.ch/record/100850/files/corelationinequality2007.pdf
LTHC
252058
U10432
oai:infoscience.tind.io:100850
article
IC
GLOBAL_SET
107423
107423
LTHC-ARTICLE-2007-033
EPFL
PUBLISHED
REVIEWED
ARTICLE