Adaptive Methods for Linear Programming Decoding

Taghavi, Mohammad Hossein; Siegel, Paul H.

doi:10.1109/tit.2008.2006384

Cited by 107 publications

(130 citation statements)

References 12 publications

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“…To further reduce the computational complexity, in 2008, Taghavi and Siegel [14] proposed an adaptive approach, called adaptive linear programming (ALP) decoding. It can be applicable to high density codes instead of the direct implementation of the original LP decoding algorithm.…”

Section: Linear Programming Decodingmentioning

confidence: 99%

“…As an approximation to ML decoding, Linear programming (LP) decoding was first proposed by Feldman et al [13]. Other LP-based decoding algorithms are developed to improve the speed or performance of Feldman et al's LP decoder [14], [15], [16], [17]. Although most of LP decoding algorithms are utilized to decode LDPC codes, they also worked very well when utilized to decode algebraic block codes, such as BCH codes, Golay codes, and the (89, 45, 17) QR code, e.g., see [15], [17], [11].…”

Section: Introductionmentioning

confidence: 99%

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Algebraic and linear programming decoding of the (73, 37, 13) quadratic residue code

Liu

Chen

et al. 2014

2014 IEEE International Conference on Communications (ICC)

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In this paper 1 , a method to search the subsets I and J needed in computing the unknown syndromes for the (73, 37, 13) quadratic residue (QR) code is proposed. According to the resulting I and J, one computes the unknown syndromes, and thus finds the corresponding error-locator polynomial by using an inverse-free BM algorithm. Based on the modified Chase-II algorithm, the performance of soft-decision decoding for the (73, 37, 13) QR code is given. This result is never seen in the literature, to our knowledge. Moreover, the error-rate performance of linear programming (LP) decoding for the (73, 37, 13) QR code is also investigated, and LP-based decoding is shown to be significantly superior in performance to the algebraic soft-decision decoding while requiring almost the same computational complexity.Index Terms-Berlekamp-Massey algorithm, quadratic residue code, Chase algorithm, linear programming.

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Section: Linear Programming Decodingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Algebraic and linear programming decoding of the (73, 37, 13) quadratic residue code

Liu

Chen

et al. 2014

2014 IEEE International Conference on Communications (ICC)

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“…d s j is the degree of symbol node s j , N l s j , andN l s j denote the set of all check nodes reached by a tree spreading from symbol node s j with in depth l, and its complement, respectively [6]. It was proved that [4] the PEG algorithm constructs Tanner graphs having a large girth and the lower bound on the girth was proved to be Algorithm 1. PEG algorithm 1: for j = 0 to n -1 do 2:…”

Section: Progressive Edge-growth Algorithmmentioning

confidence: 99%

“…Since their re-discovery, there are many methods such as the message-passing decoding and the linear program decoding [3,4] that have been proposed for the decoding algorithm. Also many other methods have been proposed for the construction algorithm [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Improved progressive edge-growth algorithm for fast encodable LDPC codes

Jiang

Lee

2012

J Wireless Com Network

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The progressive edge-growth (PEG) algorithm is known to construct low-density parity-check (LDPC) codes at finite code lengths with large girths by establishing edges between symbol and check nodes in an edge-by-edge manner. The linear-encoding PEG (LPEG) algorithm, a simple variation of the PEG algorithm, can be applied to generate linear time encodable LDPC codes whose m parity bits p 1 , p 2 , ..., p m are computed recursively in m steps. In this article, we propose modifications of the LPEG algorithm to construct LDPC codes whose number of encoding steps is independent of the code length. The maximum degree of the symbol nodes in the It has also been proved that the PEG codes and the codes proposed in this article have similar lower bound on girth. Simulation results showed that the proposed codes perform very well over the AWGN channel with an iterative decoding.

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“…Using this scheme, the number of variables and constraints for the corresponding LPD formulation grows linearly with the check degrees. Another appealing method with low complexity is the adaptive linear programming (ALP) decoding [5]. The ALP method can reduce the decoding complexity by solving a sequence of smaller LP problems.…”

Section: Introductionmentioning

confidence: 99%

Improved Check Node Decomposition for Linear Programming Decoding

Jiao

2013

IEEE Commun. Lett.

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For the linear programming decoding (LPD) proposed by Feldman et al., the number of constraints increases exponentially with check degrees. By decomposing a high-degree check node into a number of degree-3 check nodes, the number of constraints grows linearly with check degrees. In this letter, we show that the size of the LPD can be reduced by decomposing a high-degree check node into a number of degree-4 check nodes. The LPD using the degree-4 decomposition leads to almost the same number of constraints as using the degree-3 decomposition, while the number of auxiliary variable nodes is less than half of the one using the degree-3 decomposition. Moreover, when decomposing a high degree check node into a number of check nodes with degree d, d > 4, the number of constraints increases rapidly and the size of the LPD becomes larger than the degree-4 decomposition. It is demonstrated on an LDPC code and a BCH code that the decoding time of the degree-4 decomposition is the smallest among the different decomposition methods.Index Terms-Check node decomposition, linear block code, linear programming decoding (LPD), high-degree check node.

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Adaptive Methods for Linear Programming Decoding

Cited by 107 publications

References 12 publications

Algebraic and linear programming decoding of the (73, 37, 13) quadratic residue code

Algebraic and linear programming decoding of the (73, 37, 13) quadratic residue code

Improved progressive edge-growth algorithm for fast encodable LDPC codes

Improved Check Node Decomposition for Linear Programming Decoding

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