On the relation between MAP and BP GEXIT functions of low density parity check codes
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Shannon in his seminal work \cite{paper:shannon} formalized the framework on the problem of digital communication of information and storage. He quantified the fundamental limits of compression and transmission rates. The quantity \textit{channel capacity} ...
We consider communication over a binary erasure channel with low density parity check codes and optimal maximum a posteriori decoding. It is known that the problem of computing the average conditional entropy, over such code ensembles, in the asymptotic li ...
Recently the decay of correlations between bits of low density generator matrix (LDGM) codes have been investigated by using high temperature expansions from statistical physics \cite{KuMa07}. In this work we apply these ideas to a special class of low den ...
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 ...
Institute of Electrical and Electronics Engineers2007
Consider communication over a binary-input memoryless output-symmetric channel with low-density parity-check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the aver ...
Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the aver ...
We derive the average weight distribution function and its asymptotic growth rate for low-density parity-check (LDPC) code ensembles. We show that the growth rate of the minimum distance of LDPC codes depends only on the degree distribution pair. It turns ...
Interface free energy is the contribution to the free energy of a system due to the presence of an interface separating two coexisting phases at equilibrium. It is also called interfacial free energy or surface tension. The content of the paper is 1) the d ...
The spectrum of exponentially weighted covariance matrices is studied here. We first give a formal way of obtaining the spectrum using annealed approximation frequently used in Statistical Mechanics. Using the method developed by Bai and Silverstein we obt ...
This work deals with coding systems based on sparse graph codes. The key issue we address is the relationship between iterative (in particular belief propagation) and maximum a posteriori decoding. We show that between the two there is a fundamental connec ...