A separation algorithm for improved LP-decoding of linear block codes

Tanatmis, Akin; Ruzika, Stefan; Hamacher, Horst W.; Punekar, Mayur; Kienle, Frank; Wehn, Norbert

doi:10.1109/turbocoding.2008.4658669

Cited by 12 publications

(33 citation statements)

References 22 publications

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“…To demonstrate the improvement offered by the proposed RPC search algorithm, we compare its error-correcting performance to that of LP/ALP decoding , BP decoding (sumproduct algorithm with a maximum of 1000 iterations), the Separation Algorithm (SA) [4], and ML decoding for two [8].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…. , m of the parity-check matrix, corresponding to a check node in the associated Tanner graph, the linear inequalities used to form the fundamental polytope P are given by (4) where N (j) ⊆ {1, 2, . .…”

Section: A Lp Relaxation Of ML Decodingmentioning

confidence: 99%

“…In fact, the average number of random trials needed to find an RPC cut grows exponentially with the code length. The separation algorithm in [4] provides another way to search for RPC cuts, but in many cases the RPC cuts found by this algorithm do not lead to an integral solution, and therefore it provides only limited performance improvement. Motivated by the Cut Search Algorithm introduced in Section III-A, we next propose a new, efficient RPC cut-generating algorithm that has been found empirically to provide useful RPC cuts.…”

Section: B Generating Cut-inducing Rpcsmentioning

confidence: 99%

“…However, the random nature of this algorithm limits its efficiency. Recently, authors in [4] proposed a separation algorithm which searches immediately for cuts that can be derived from an arbitrarily chosen dual codeword during each iteration of the LP decoding problem, and these cuts improve the error-correcting performance of the original LP decoder.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive cut generation for improved linear programming decoding of binary linear codes

Zhang

Siegel

2011

2011 IEEE International Symposium on Information Theory Proceedings

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Linear programming (LP) decoding approximates optimal maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of linear inequalities derived from the constraints represented by the rows of a parity-check matrix of the code. Adaptive linear programming (ALP) decoding significantly reduces the complexity of LP decoding by iteratively and adaptively adding necessary constraints in a sequence of smaller LP problems. Adaptive introduction of constraints derived from certain additional redundant parity check (RPC) constraints can further improve ALP performance. In this paper, we propose a new and effective algorithm to identify RPCs that produce linear constraints, referred to as "cuts," that can eliminate non-ML solutions generated by the ALP decoder, often significantly improving the decoder error-rate performance. The cut-finding algorithm is based upon a specific transformation of an initial parity-check matrix of the linear block code. Simulation results for several low-density parity-check codes demonstrate that the modified ALP decoding algorithm significantly narrows the performance gap between LP decoding and ML decoding.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: A Lp Relaxation Of ML Decodingmentioning

confidence: 99%

Section: B Generating Cut-inducing Rpcsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive cut generation for improved linear programming decoding of binary linear codes

Zhang

Siegel

2011

2011 IEEE International Symposium on Information Theory Proceedings

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“…In practice, the τ R/I p [i]'s can be chosen to be a small constant or optimized online by lifting it into the objective function. Of course, the 2 -norm could also be used in (26), which is optimal for AWGN, at the cost of higher complexity (as convex quadratic programming, usually solved by secondorder cone programming methods).…”

Section: Pilot Constraints Under Noisementioning

confidence: 99%

On Efficient Utilization of Training Pilots for Linear Equalization of QAM Transmissions

Jacklin

Ding

2013

IEEE Trans. Commun.

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Conventional approaches to linear equalization of data transmissions under frequency selective channels simply treat the problem as a system identification issue. However, practical data communication systems impose additional conditions on the channel input signals such as LDPC error correction coding and known data constellation. We study a unified framework to integrate these known constraints into the channel equalization procedure and propose a linear programming-based approach to channel equalization for QAM signals that can succeed with significantly reduced pilots. In addition to utilizing the information of QAM constellation, our method exploits the code information of LDPC forward error correction coding to improve the equalization performance and convergence properties.

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