Addendum to “An Efficient Algorithm to Find All Small-Size Stopping Sets of Low-Density Parity-Check Matrices”

Rosnes, Eirik; Ytrehus, Øyvind; Ambroze, Marcel; Tomlinson, M.

doi:10.1109/tit.2011.2171531

Cited by 28 publications

(43 citation statements)

References 9 publications

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“…The quality of this solution depends on the problem size and the time-limit used. It should be noted that, for long LDPC codes, obtaining an exhaustive, or at least sufficiently comprehensive, list of smallsize stopping sets may also be very time-consuming [10], [13], [14]. This means that for such codes it may take a long time to obtain a list L of small-size stopping sets.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The list L, which ordinarily contains small stopping sets of size less than some threshold, can be constructed, for example, using methods given in [10], [13], [14]. Our ILP-based approach returns a row that removes the highest number of stopping sets in L. The new row may or may not be in the dual (orthogonal) code C ⊥ (i.e., the new row can or cannot be expressed as a linear combination of the rows of H).…”

Section: An Ilp-based Approach For Eliminating Stopping Setsmentioning

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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Section: Simulation Resultsmentioning

confidence: 99%

Section: An Ilp-based Approach For Eliminating Stopping Setsmentioning

confidence: 99%

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

Falsafain

Mousavi

2015

IEEE Trans. Commun.

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“…. , 33} and compute the corresponding minimum Hamming distance using the algorithm in [7], [8], until d qc = 16 is obtained. The 3 × 5 base-prototype matrix The IEEE 802.16e standard [6] provides a class of welldesigned QC-LDPC codes.…”

Section: B Design Examplementioning

confidence: 99%

“…(13) to modify the right circulant permutations given by b n (i, j) that are specified as entries in H b , for all 0 ≤ i ≤ m b − 1, 0 ≤ j ≤ n b − 1, and circulant size z = 96 × n/2304. From [8], the rate-1/2 code of n = 1152 and z = 48 is a good candidate for our lattice construction, since d qc = 16.…”

Section: B Design Examplementioning

confidence: 99%

“…The modification to the 12 × 24 base-prototype matrix of rate-1/2 codes is shown in Table I, where the appended block row S consisting of S j , 0 ≤ j ≤ 23, can be expanded to a 24 × 1152 submatrix of the form in (3). We selected the block rows 1, 4, 8 and 10 to be modified by replacing four specific zero matrices (for which b(i, j) = −1) with the four CPMs: Q b (1,12) , Q b (4,15) , Q b (8,18) and Q b (10,19) . To remove overlap of CPMs in one block column among the selected block rows, a CPM P b (1,6) is replaced with a zero matrix denoted by Q −1 .…”

Section: B Modification To Ieee 80216e Qc-ldpc Codesmentioning

confidence: 99%

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Construction D′ Lattices from Quasi-Cyclic Low-Density Parity-Check Codes

Chen

Kurkoski

Rosnes

2018

2018 IEEE 10th International Symposium on Turbo Codes &Amp; Iterative Information Processing (ISTC)

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Recently, Branco da Silva and Silva described an efficient encoding and decoding algorithm for Construction D lattices. Using their algorithm, we propose a Construction D lattice based on binary quasi-cyclic low-density parity-check (QC-LPDC) codes and single parity-check product codes. The underlying codes designed by the balanced-distances rule contribute in a balanced manner to the squared minimum distance of the constructed lattice, which results in a high lattice coding gain. The proposed lattice based on IEEE 802.16e QC-LDPC codes is shown to provide competitive error-rate performance on the power-unconstrained additive white Gaussian noise channel.

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On the complexity of and solutions to the minimum stopping and trapping set problems

Velasquez

Subramani

Wojciechowski

2022

Theoretical Computer Science

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Addendum to “An Efficient Algorithm to Find All Small-Size Stopping Sets of Low-Density Parity-Check Matrices”

Cited by 28 publications

References 9 publications

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

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

Construction D′ Lattices from Quasi-Cyclic Low-Density Parity-Check Codes

On the complexity of and solutions to the minimum stopping and trapping set problems

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