Improved Probabilistic Bounds on Stopping Redundancy

Han, Junsheng; Siegel, Paul H.; Vardy, Alexander

doi:10.1109/tit.2008.917624

Cited by 25 publications

(27 citation statements)

References 16 publications

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“…For the same reason, such rows can eliminate only stopping sets that are not equal to the support set of a codeword. In [14] and [6], upper bounds on the number of redundant rows needed to ensure that the weight of the smallest stopping set is the minimum distance of the code, were derived. In [10], an algorithm that finds redundant rows, named "Genie-aided random search" (GARS), was described.…”

Section: Finding Low Weight Redundant Rowsmentioning

confidence: 99%

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Decreasing error floor in LDPC codes by parity-check matrix extensions

Fainzilber

Sharon

Litsyn

2009

2009 IEEE International Symposium on Information Theory

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High error floors in optimized irregular LDPC codes limit their usage in applications that require low error rates. We introduce new methods for lowering the error floor of LDPC codes, based on enhancing the code's parity-check matrix with additional linearly dependent and independent parity-checks. We prove NP hardness of certain optimization problems related to proposed methods and provide upper bound on the number of parity-checks that need to be added. We show that the proposed methods can lower the error floor of the code significantly, by several orders of magnitude, at negligible or no rate penalty.

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Section: Finding Low Weight Redundant Rowsmentioning

confidence: 99%

“…ISIT 2009, Seoul, Korea, June 28 -July 3,2009 %list of stopping sets that will be reactivated by v: Next, by using similar methods to the ones described in [6], we derive an upper bound on the minimal number of paritychecks required in order to eliminate a set 5 of stopping sets (i.e. an upper bound on IAMSSE(V, 5)1).…”

Section: Table I Gars and Lwrrs Algorithmsmentioning

confidence: 99%

Decreasing error floor in LDPC codes by parity-check matrix extensions

Fainzilber

Sharon

Litsyn

2009

2009 IEEE International Symposium on Information Theory

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“…In this work, we first propose an improvement to the upper bounds in [7], [8]. While the upper bounds in [7], [8] are obtained by probabilistic methods, in our approach, we initially select a few first rows deterministically and then continue along the lines of probabilistic analysis in [7], [8].…”

Section: Introductionmentioning

confidence: 99%

Stopping Redundancy Hierarchy Beyond the Minimum Distance

Yakimenka

Skachek

Bocharova

et al. 2019

IEEE Trans. Inform. Theory

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Stopping sets play a crucial role in failure events of iterative decoders over a binary erasure channel (BEC). The -th stopping redundancy is the minimum number of rows in the parity-check matrix of a code, which contains no stopping sets of size up to . In this work, a notion of coverable stopping sets is defined. In order to achieve maximum-likelihood performance under iterative decoding over the BEC, the paritycheck matrix should contain no coverable stopping sets of size , for 1 ≤ ≤ n − k, where n is the code length, k is the code dimension. By estimating the number of coverable stopping sets, we obtain upper bounds on the -th stopping redundancy, 1 ≤ ≤ n − k. The bounds are derived for both specific codes and code ensembles. In the range 1 ≤ ≤ d − 1, for specific codes, the new bounds improve on the results in the literature. Numerical calculations are also presented. are also with ITMO, St. Petersburg, Russian Federation.The results of this work were partly presented in [1].

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“…The size of the smallest stopping set, as well as the distribution of stopping set sizes, depends on the particular form of the parity-check matrix used for decoding. Since including a large number of rows in the parity-check matrix of a code ensures increased flexibility in meeting predefined constraints on the structure of stopping sets, several authors recently proposed the use of redundant parity-check matrices for improving the performance of iterative decoders [2], [3], [4], [5], [6]. The effects of augmenting the sets of parity-checks in matrices from random ensembles were also studied in [7], [8].…”

Section: Introductionmentioning

confidence: 99%

Permutation Decoding and the Stopping Redundancy Hierarchy of Linear Block Codes

Hehn

Milenković

Laendner

et al. 2007

2007 IEEE International Symposium on Information Theory

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We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the trade-off between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for the stopping redundancy hierarchy via Lovász's Local Lemma and Bonferroni-type inequalities, and specialize them for codes with cyclic parity-check matrices. Based on the observed properties of parity-check matrices with good stopping redundancy characteristics, we develop a novel decoding technique, termed automorphism group decoding, that combines iterative message passing and permutation decoding. We also present bounds on the smallest number of permutations of an automorphism group decoder needed to correct any set of erasures up to a prescribed size. Simulation results demonstrate that for a large number of algebraic codes, the performance of the new decoding method is close to that of maximum likelihood decoding.

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Improved Probabilistic Bounds on Stopping Redundancy

Cited by 25 publications

References 16 publications

Decreasing error floor in LDPC codes by parity-check matrix extensions

Decreasing error floor in LDPC codes by parity-check matrix extensions

Stopping Redundancy Hierarchy Beyond the Minimum Distance

Permutation Decoding and the Stopping Redundancy Hierarchy of Linear Block Codes

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