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On the Joint Decoding of LDPC Codes and Finite-State Channels via Linear Programming

In this paper, the linear programming (LP) decoder for binary linear codes, introduced by Feldman, et al. is extended to joint-decoding of binary-input finite-state channels. In particular, we provide a rigorous definition of LP joint-decoding pseudo-codewords (JD-PCWs) that enables evaluation of the pairwise error probability between codewords and JD-PCWs. This leads naturally to a provable upper bound on decoder failure probability. If the channel is a finite-state intersymbol interference channel, then the LP joint decoder also has the maximum-likelihood (ML) certificate property and all integer valued solutions are codewords. In this case, the performance loss relative to ML decoding can be explained completely by fractional valued JD-PCWs.

preprint2010arXivOpen access
Byung-Hak KimHenry D. Pfister
math.ITInformation Theory
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Byung-Hak KimHenry D. Pfister

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