Eliminating small stopping sets in irregular low-density parity-check codes

Jiao, Xiaopeng; Mu, Jianjun; Jun, Song; Zhou, Lihua

doi:10.1109/lcomm.2009.090009

Cited by 21 publications

(17 citation statements)

References 10 publications

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“…One category of such literature, focusses on modification of iterative decoding algorithms, see, e.g., [9], while another category is concerned with the code construction. In the second category, some researchers use indirect measures such as girth [18] or approximate cycle extrinsic message degree (ACE) [19], while others work with direct measures of error floor performance such as the distribution of stopping sets or trapping sets [20], [10], [11]. In [20], edge swapping is proposed as a technique to increase the stopping distance of an LDPC code, and thus to improve its error floor performance over the BEC.…”

Section: Introductionmentioning

confidence: 99%

Lowering the Error Floor of LDPC Codes Using Cyclic Liftings

Asvadi

Banihashemi

Ahmadian-Attari

2011

IEEE Trans. Inform. Theory

105

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Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which form the trapping sets. We derive a necessary and sufficient condition for the cyclic permutations assigned to the edges of a cycle c of length ℓ(c) in the base graph such that the inverse image of c in the lifted graph consists of only cycles of length strictly larger than ℓ(c). The proposed method is universal in the sense that it can be applied to any LDPC code over any channel and for any iterative decoding algorithm. It also preserves important properties of the base code such as degree distributions, encoder and decoder structure, and in some cases, the code rate. The proposed method is applied to both structured and random codes over the binary symmetric channel (BSC). The error floor improves consistently by increasing the lifting degree, and the results show significant improvements in the error floor compared to the base code, a random code of the same degree distribution and block length, and a random lifting of the same degree. Similar improvements are also observed when the codes designed for the BSC are applied to the additive white Gaussian noise (AWGN) channel.

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Section: Introductionmentioning

confidence: 99%

Lowering the Error Floor of LDPC Codes Using Cyclic Liftings

Asvadi

Banihashemi

Ahmadian-Attari

2011

IEEE Trans. Inform. Theory

105

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show abstract

“…This means that for such codes it may take a long time to obtain a list L of small-size stopping sets. For comparison purposes, we also present the results of the algorithm given by Jiao et al in [8]. The simulations were carried out over the BEC using iterative edge-removal algorithm (100 block errors were collected per point).…”

Section: Simulation Resultsmentioning

confidence: 99%

“…1 shows the block error rate (BLER) performance improvement offered by augmentation of the paritycheck matrix H 1 by the new row. The method described in [8] provides a row which removes the same number of stopping sets. However, it cannot eliminate all size-4 stopping sets in L.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Current stopping set elimination methods (e.g., the methods described in [8], [10]) may have no regard for the girth of the Tanner graph, and they may introduce new 4-cycles. In the example mentioned in the previous paragraph, extending the parity-check matrix by the new rows introduces 63208 new 4-cycles, while the original Tanner graph has only 240 4-cycles.…”

Section: A Limiting the Weight Of The New Row And Avoiding 4-cyclesmentioning

confidence: 99%

“…In [7], Fainzilber et al proposed a method for finding low-weight redundant rows that eliminate a reasonably large number of stopping sets in a given list of stopping sets of a parity-check matrix H, which brings into play a low-density generator matrix of the null-space of H. They also presented a greedy inexact algorithm for finding independent parity-check rows that do so. In [8], Jiao et al presented a simple heuristic algorithm for eliminating small stopping sets in irregular LDPC codes, by introducing new independent check nodes into the original Tanner graph. To construct these new nodes, the algorithm makes use of the frequency of each variable node in a given list of stopping sets.…”

Section: Introductionmentioning

confidence: 99%

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Stopping Set Elimination by Parity-Check Matrix Extension via Integer Linear Programming

Falsafain

Mousavi

2015

IEEE Trans. Commun.

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Error-rate floor phenomenon is known to be a serious impediment to the use of low-density parity-check (LDPC) codes for some practical applications that demand high data reliability. In the case of binary erasure channels (BECs), certain error-prone patterns, known as stopping sets, are proven to cause this performance degradation. A possible approach to diminish this drawback over BECs is to eliminate stopping sets by parity-check matrix extension. Given a parity-check matrix H, and a list L of its stopping sets, we present an integer linear programming (ILP) formulation to find a parity-check equation which eliminates the maximum number of stopping sets in L. One of the distinguishing advantages of the proposed scheme is its flexibility for modifications such as: limiting the weight of the new parity-check row, making the new row redundant or linearly independent, 4-cycle avoidance, and taking into account the sizes of stopping sets. Armed with these adjustments, the method can provide good performance improvements, as evidenced by simulation results. Furthermore, for a given ∈ N, by extending the basic formulation, we provide an ILP formulation for finding a set of size of parity-check equations which can best eliminate the stopping sets in L, among all such sets.Index Terms-Binary erasure channel, error floor, integer linear programming, LDPC code, stopping set.

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A construction of LDPC codes with low error floors

Yeh

Chen

2013

2013 International Conference on Advanced Technologies for Communications (ATC 2013)

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Eliminating small stopping sets in irregular low-density parity-check codes

Cited by 21 publications

References 10 publications

Lowering the Error Floor of LDPC Codes Using Cyclic Liftings

Lowering the Error Floor of LDPC Codes Using Cyclic Liftings

Stopping Set Elimination by Parity-Check Matrix Extension via Integer Linear Programming

A construction of LDPC codes with low error floors

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