Stopping set distribution of LDPC code ensembles

Orlitsky, A.; Viswanathan, K.; Zhang, J.

doi:10.1109/isit.2003.1228137

Cited by 60 publications

(124 citation statements)

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“…Divsalar also extended the enumerator technique in [9] to stopping set enumerators in [11], [12]. Analogous to the role of ensemble weight enumerators in determining average code performance on Gaussian channel, stopping set [13] enumerators determine the performance of LDPC codes under iterative decoding on the binary erasure channel (BEC) [13]- [15] and the burst-erasure channel. A generalization of the notion of a stopping set, called a generalized stopping set, was introduced in [16] and used to evaluate the performance of G-LDPC codes with a single constraint type.…”

Section: Introductionmentioning

confidence: 99%

Ensemble Enumerators for Protograph-Based Generalized LDPC Codes

Abu‐Surra

Ryan

2007

IEEE GLOBECOM 2007-2007 IEEE Global Telecommunications Conference

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Protograph-based LDPC codes have the advantages of a simple design (or search) procedure and highly structured encoders and decoders. These advantages have also been exploited in the design of protograph-based generalized LDPC (G-LDPC) codes. Recently, a technique for computing ensemble weight enumerators and stopping set enumerators for protograph-based LDPC codes has been published. In the current paper, we extend those results to protograph-based G-LDPC codes. That is, we first derive ensemble weight and stopping set enumerators for finite-length G-LDPC codes based on protographs, and then we consider the asymptotic case. In the weight enumerator case, the asymptotic results allow us to determine whether or not the typical minimum distance in the ensemble grows linearly with codeword length. In the stopping set enumerator case, the asymptotic results allows us to determine whether or not the typical smallest stopping set size grows linearly with codeword length.

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Section: Introductionmentioning

confidence: 99%

Ensemble Enumerators for Protograph-Based Generalized LDPC Codes

Abu‐Surra

Ryan

2007

IEEE GLOBECOM 2007-2007 IEEE Global Telecommunications Conference

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“…If there are no VNs of degree 2, such "good" spectral shape behavior is guaranteed; however, good codes from a threshold point of view have a positive fraction of degree-2 VNs [9]. For unstructured irregular ensembles with λ 2 > 0, the slope of the curve at α = 0 is given by G (0) = log(λ 2 ρ (1)); thus we require λ 2 ρ (1) < 1 in order to avoid a problematic weight distribution [42,43].…”

Section: Figure 11mentioning

confidence: 99%

“…It was shown in [42,43] that the minimum distance of a code chosen at random from the ensemble is approximately α * n (and thus growing linearly with n) with a positive probability when λ 2 ρ (1) < 1 (the actual probability being √ 1 − λ 2 ρ (1) in this case), but with probability 0 when λ 2 ρ (1) > 1. It is interesting to note that for protograph codes, the condition λ 2 ρ (1) < 1 is sufficient but not necessary for linear minimum distance growth [17].…”

Section: Example 12mentioning

confidence: 99%

“…The weight distribution analyses mentioned above can be easily modified to yield instead the stopping set size distribution, simply by replacing the WEFs of the CNs by the corresponding stopping set enumerating functions (SSEFs)-some results for the unstructured irregular LDPC code ensemble are reported in [43]. Thus, for the unstructured irregular LDPC ensemble, we need only replace each…”

Section: Example 12mentioning

confidence: 99%

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Low-Density Parity-Check Code Constructions

Flanagan

2014

Academic Press Library in Mobile and Wireless Communications

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“…Di et al [7] examine iterative decoding of LDPC codes over the binary erasure channel and establish that stopping sets play a crucial role in its analysis. Consequently the determination of stopping sets in codes from finite geometries and designs, and indeed from LDPC codes in general, has been of interest [20,23,28]. Of particular concern has been the size of the smallest nonempty stopping set.…”

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confidence: 99%

Small stopping sets in Steiner triple systems

Colbourn

Fujiwara

2008

Cryptogr. Commun.

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The size of the smallest stopping set in a low-density parity check (LDPC) code determines, to an extent, the performance of iterative decoding methods over the binary erasure channel. In an LDPC code arising from a block design, a stopping set is a subset of its blocks with the property that every point belonging to one of the selected blocks belongs to at least two of them. While some Steiner triple systems have no stopping sets of size 5 or less, it is shown that every Steiner triple system has a stopping set of size at most 7. The proof can be viewed as an application of polynomial identities among configuration counts that generalize the family of known linear identities. While no example of a Steiner triple system whose smallest stopping set has size seven is known, it is shown that a partial Steiner triple system on v points with c · v 1.8 triples that has no stopping set of size less than 7 exists.

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Stopping set distribution of LDPC code ensembles

Cited by 60 publications

References 1 publication

Ensemble Enumerators for Protograph-Based Generalized LDPC Codes

Ensemble Enumerators for Protograph-Based Generalized LDPC Codes

Low-Density Parity-Check Code Constructions

Small stopping sets in Steiner triple systems

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