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How to prove the Maxwell conjecture via spatial coupling — A proof of concept | IEEE Conference Publication | IEEE Xplore
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How to prove the Maxwell conjecture via spatial coupling — A proof of concept


Abstract:

Investigations on spatially coupled codes have lead to the conjecture that, in the infinite size limit, the average input-output conditional entropy for spatially coupled...Show More

Abstract:

Investigations on spatially coupled codes have lead to the conjecture that, in the infinite size limit, the average input-output conditional entropy for spatially coupled low-density parity-check ensembles, over binary memoryless symmetric channels, equals the entropy of the underlying individual ensemble. We give a self-contained proof of this conjecture for the case when the variable degrees have a Poisson distribution and all check degrees are even. The ingredients of the proof are the interpolation method and the Nishimori identities. We explain why this result is an important step towards proving the Maxwell conjecture in the theory of low-density parity-check codes.
Date of Conference: 01-06 July 2012
Date Added to IEEE Xplore: 27 August 2012
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Conference Location: Cambridge, MA, USA

References

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