NDLI: Joint Decoding of LDPC Codes and Finite-State Channels Via Linear-Programming

Content Provider	IEEE Xplore Digital Library
Author	Byung-Hak Kim Pfister, H.D.
Copyright Year	2007
Abstract	This paper considers the joint-decoding problem for finite-state channels (FSCs) and low-density parity-check (LDPC) codes. In the first part, the linear-programming (LP) decoder for binary linear codes is extended to perform joint-decoding of binary-input FSCs. 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 in AWGN. This leads naturally to a provable upper bound on decoder failure probability. If the channel is a finite-state intersymbol interference channel, then the joint LP 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. After deriving these results, we discovered some elements were equivalent to earlier work by Flanagan on linear-programming receivers. In the second part, we develop an efficient iterative solver for the joint LP decoder discussed in the first part. In particular, we extend the approach of iterative approximate LP decoding, proposed by Vontobel and Koetter and analyzed by Burshtein, to this problem. By taking advantage of the dual-domain structure of the joint-decoding LP, we 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 per-iteration complexity is similar to that of TE but whose performance is similar to that of joint LP decoding. The main advantage of this decoder is that it appears to provide the predictability and superior performance of joint LP decoding with the computational complexity of TE. One expected application is coding for magnetic storage where the required block-error rate is extremely low and system performance is difficult to verify by simulation.
Sponsorship	IEEE Signal Processing Society
Starting Page	1563
Ending Page	1576
Page Count	14
File Size	977238
File Format	PDF
ISSN	19324553
Volume Number	5
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Iterative decoding Linear programming Parity check codes Maximum likelihood decoding Pairwise error probability Intersymbol interference turbo equalization BCJR algorithm finite-state channels joint-decoding low-density parity-check (LDPC) codes linear-programming (LP) decoding
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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