An Iterative Joint Linear-Programming Decoding of LDPC Codes and Finite-State Channels

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In this paper, the authors introduce an efficient iterative solver for the joint Linear-Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes and Finite-State Channels (FSCs). In particular, they extend the approach of iterative approximate LP decoding, proposed by Vontobel and Koetter and explored by Burshtein, to this problem. By taking advantage of the dual-domain structure of the joint decoding LP, they obtain a convergent iterative algorithm for joint LP decoding whose structure is similar to BCJR-based Turbo Equalization (TE). The result is a joint iterative decoder whose complexity is similar to TE but whose performance is similar to joint LP decoding.