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Abstract: We address the problem of the joint sequence detection in partial-responsePR channels and decoding of low-density parity-check LDPC codes. We modelthe PR channel and the LDPC code as a combined inference problem. We presentfor the first time the derivation of the belief propagation BP equations thatallow the simultaneous detection and decoding of a LDPC codeword in a PRchannel. To accomplish this we follow an approach from statistical mechanics,in which the Bethe free energy is minimized with respect to the beliefs on thenodes of the PR-LDPC graph. The equations obtained are explicit and are optimalfor decoding LDPC codes on PR channels with polynomial $hD = 1 - a D^n$ areal, n positive integer in the sense that they provide the exact inference ofthe marginal probabilities on the nodes in a graph free of loops. A simplealgorithmic solution to the set of BP equations is proposed and evaluated usingnumerical simulations, yielding bit-error rate performances that surpass thoseof turbo equalization.



Author: Jaime A. Anguita, Michael Chertkov, Mark A. Neifeld, Bane Vasic

Source: https://arxiv.org/







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