Symmetrical Constructions for Regular Girth-8 QC-LDPC Codes

Tasdighi, Alireza; Banihashemi, Amir H.; Sadeghi, Mohammad‐Reza

doi:10.1109/tcomm.2016.2617335

Cited by 42 publications

(53 citation statements)

References 16 publications

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“…In Table 8, we compare the performance of BC 3 with some commonly used methods from the literature. The (J, K)-regular codes in [29,30] are generated by carrying out complete enumeration, which is the common method for code generation in the telecommunications literature, for the mentioned (m, n) dimensions in Table 8. There are several criteria to pick the best LDPC code: small (m, n) dimensions and regular degree distributions (easier hardware implementation), small (J, K) values (faster decoding with a sparse code), and high girth g (better error correction).…”

Section: Computational Resultsmentioning

confidence: 99%

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A branch‐and‐cut algorithm for a bipartite graph construction problem in digital communication systems

2019

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We study a bipartite graph (BG) construction problem that arises in digital communication systems. In a digital communication system, information is sent from one place to another over a noisy communication channel using binary symbols (bits). The original information is encoded by adding redundant bits, which are then used to detect and correct errors that may have been introduced during transmission. Harmful structures, such as small cycles, severely deteriorate the error correction capability of a BG. We introduce an integer programming formulation to generate a BG for a given smallest cycle length. We propose a branch-and-cut algorithm for its solution and investigate the structural properties of the problem to derive valid inequalities and variable fixing rules. We also introduce heuristics to obtain feasible solutions for the problem. The computational experiments show that our algorithm can generate BGs without small cycles in an acceptable amount of time for practically relevant dimensions.

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Section: Computational Resultsmentioning

confidence: 99%

“…In Table 8, we consider the (J, K), (m, n), and g parameters used in [29,30], and implement our BC 3 method to solve the instances to optimality without any time limitations. We do not utilize Polish heuristic, since there is no solution pool.…”

Section: Computational Resultsmentioning

confidence: 99%

A branch‐and‐cut algorithm for a bipartite graph construction problem in digital communication systems

2019

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“…Recently, QC-LDPC codes with girth 8, whose parity-check matrices have some symmetries, and are in many cases shorter than previously existing girth-8 QC-LDPC codes, were constructed in [29]. We tested the codes of [29], and observed that our proposed algorithm can find the exact s min , or obtain lower and upper bounds on s min , for many of them in a matter of seconds or minutes. For example, we have found the stopping distances of all 18 codes with d v = 3, g = 8,…”

Section: B Upper Bound On the Stopping Distance Of Ldpc Codesmentioning

confidence: 99%

“…R ≤ 0.88 and n ≤ 4000 (Table I of [29]), each in less than or about one minute. The last code in that table is C 13 in Table V.…”

Section: B Upper Bound On the Stopping Distance Of Ldpc Codesmentioning

confidence: 99%

Characterization and Efficient Search of Non-Elementary Trapping Sets of LDPC Codes With Applications to Stopping Sets

Hashemi

Banihashemi

2019

IEEE Trans. Inform. Theory

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In this paper, we propose a characterization for non-elementary trapping sets (NETSs) of lowdensity parity-check (LDPC) codes. The characterization is based on viewing a NETS as a hierarchy of embedded graphs starting from an ETS. The characterization corresponds to an efficient search algorithm that under certain conditions is exhaustive. As an application of the proposed characterization/search, we obtain lower and upper bounds on the stopping distance s min of LDPC codes. We examine a large number of regular and irregular LDPC codes, and demonstrate the efficiency and versatility of our technique in finding lower and upper bounds on, and in many cases the exact value of, s min . Finding s min , or establishing search-based lower or upper bounds, for many of the examined codes are out of the reach of any existing algorithm.

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“…It is shown in [8] that the complexity of exhaustively checking equations of the type (2) goes exponentially high by increasing each one of the parameters m, n or N . Solutions with reduced complexity where proposed, for example, in [9], [10], but the corresponding design methods result in g = 8.…”

Section: Columnsmentioning

confidence: 99%

Efficient Search of Compact QC-LDPC and SC-LDPC Convolutional Codes With Large Girth

et al. 2018

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We propose a low-complexity method to find quasicyclic low-density parity-check block codes with girth 10 or 12 and shorter length than those designed through classical approaches. The method is extended to time-invariant spatially coupled low-density parity-check convolutional codes, permitting to achieve small syndrome former constraint lengths. Several numerical examples are given to show its effectiveness.

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Symmetrical Constructions for Regular Girth-8 QC-LDPC Codes

Cited by 42 publications

References 16 publications

A branch‐and‐cut algorithm for a bipartite graph construction problem in digital communication systems

A branch‐and‐cut algorithm for a bipartite graph construction problem in digital communication systems

Characterization and Efficient Search of Non-Elementary Trapping Sets of LDPC Codes With Applications to Stopping Sets

Efficient Search of Compact QC-LDPC and SC-LDPC Convolutional Codes With Large Girth

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