Hardness of Approximation Results for the Problem of Finding the Stopping Distance in Tanner Graphs

Krishnan, K. Murali; Chandran, L. Sunil

doi:10.1007/11944836_9

Cited by 6 publications

(7 citation statements)

References 13 publications

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“…We start by showing that MinStop is not approximable within o(log N ), where N denotes the description length of the problem, unless P = N P . This results improves upon the finding in [27], where the weaker claim that MinStop cannot be approximated within any positive constant was proved. This improvement is a consequence of the fact that our proof relies on reduction from the MinSetCov, rather than the MinVertCov problem [27].…”

Section: Hardness Of Approximation For Minstopsupporting

confidence: 87%

“…Hardness under Stronger Assumptions: Under the assumption that N P ⊂ DT IM E(N polylog N ), it was shown in [27] that there exists no polynomial time approximation algorithm for MinStop within 2 (log N ) 1−ǫ , for any ǫ > 0.…”

Section: Hardness Of Approximation For Minstopmentioning

confidence: 99%

“…The main contributions of our work are three-fold. First, we improve upon the hardness results for approximating stopping sets, presented in [27]. Furthermore, we introduce the notion of a cover stopping set, and show that the problem of finding such a set of smallest cardinality in an arbitrary Tanner graph is NP-hard.…”

Section: Introductionmentioning

confidence: 98%

“…Recently, it was shown that the problem of finding the smallest stopping set in an arbitrary code graph is NP-hard to approximate up to a constant term [27]. In [40], it was shown that finding the smallest k-out set, which represents a straightforward generalization of the notion of a stopping set, is NP-hard as well.…”

Section: Introductionmentioning

confidence: 99%

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On the Hardness of Approximating Stopping and Trapping Sets

McGregor

Milenković

2010

IEEE Trans. Inform. Theory

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We prove that approximating the size of stopping and trapping sets in Tanner graphs of linear block codes, and more restrictively, the class of low-density parity-check (LDPC) codes, is NP-hard. The ramifications of our findings are that methods used for estimating the height of the error-floor of moderate-and long-length LDPC codes based on stopping and trapping set enumeration cannot provide accurate worst-case performance predictions.

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Section: Hardness Of Approximation For Minstopsupporting

confidence: 87%

Section: Hardness Of Approximation For Minstopmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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On the Hardness of Approximating Stopping and Trapping Sets

McGregor

Milenković

2010

IEEE Trans. Inform. Theory

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“…While the knowledge of the problematic sets that dominate the error floor performance is most helpful in the design and analysis of LDPC codes, attaining such knowledge, regardless of differences in the graphical structure of these sets, is a hard problem. For instance, it was shown in [27], [20], [23] that the problem of finding a minimum size stopping set is NP hard. McGregor and Milenkovic [23] showed that not only the problem of finding a minimum size trapping set, but also the problem of approximating the size of a minimal trapping set is NP hard, regardless of the sparsity of the underlying graph.…”

mentioning

confidence: 99%

Efficient Algorithm for Finding Dominant Trapping Sets of LDPC Codes

Karimi

Banihashemi

2012

IEEE Trans. Inform. Theory

112

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This paper presents an efficient algorithm for finding the dominant trapping sets of a low-density parity-check (LDPC) code. The algorithm can be used to estimate the error floor of LDPC codes or to be used as a tool to design LDPC codes with low error floors. For regular codes, the algorithm is initiated with a set of short cycles as the input. For irregular codes, in addition to short cycles, variable nodes with low degree and cycles with low approximate cycle extrinsic message degree (ACE) are also used as the initial inputs. The initial inputs are then expanded recursively to dominant trapping sets of increasing size. At the core of the algorithm lies the analysis of the graphical structure of dominant trapping sets and the relationship of such structures to short cycles, low-degree variable nodes and cycles with low ACE. The algorithm is universal in the sense that it can be used for an arbitrary graph and that it can be tailored to find a variety of graphical objects, such as absorbing sets and Zyablov-Pinsker (ZP) trapping sets, known to dominate the performance of LDPC codes in the error floor region over different channels and for different iterative decoding algorithms. Simulation results on several LDPC codes demonstrate the accuracy and efficiency of the proposed algorithm. In particular, the algorithm is significantly faster than the existing search algorithms for dominant trapping sets.

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