Math @ Duke

Publications [#319357] of Henry Pfister
Papers Published
 Kim, BH; Pfister, HD, Joint decoding of LDPC codes and finitestate channels via linearprogramming,
Ieee Journal of Selected Topics in Signal Processing, vol. 5 no. 8
(December, 2011),
pp. 15631576, Institute of Electrical and Electronics Engineers (IEEE) [doi]
(last updated on 2019/07/21)
Abstract: This paper considers the jointdecoding problem for finitestate channels (FSCs) and lowdensity paritycheck (LDPC) codes. In the first part, the linearprogramming (LP) decoder for binary linear codes is extended to perform jointdecoding of binaryinput FSCs. In particular, we provide a rigorous definition of LP jointdecoding pseudocodewords (JDPCWs) that enables evaluation of the pairwise error probability between codewords and JDPCWs in AWGN. This leads naturally to a provable upper bound on decoder failure probability. If the channel is a finitestate intersymbol interference channel, then the joint LP decoder also has the maximumlikelihood (ML) certificate property and all integervalued solutions are codewords. In this case, the performance loss relative to ML decoding can be explained completely by fractionalvalued JDPCWs. After deriving these results, we discovered some elements were equivalent to earlier work by Flanagan on linearprogramming 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 dualdomain structure of the jointdecoding LP, we obtain a convergent iterative algorithm for joint LP decoding whose structure is similar to BCJRbased turbo equalization (TE). The result is a joint iterative decoder whose periteration 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 blockerror rate is extremely low and system performance is difficult to verify by simulation. © 2011 IEEE.


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