High Speed Low Error Floor Hardware Implementation and Fast and Accurate Error Floor Estimation of LDPC Decoders

Tolouei, Sina

doi:10.22215/etd/2014-10497

Cited by 3 publications

(2 citation statements)

References 63 publications

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“…for each variable node v ∈ V do 5: are connected to only one satisfied check node [23], [1], [16], [19], [32], [9]. This is particularly the case for irregular codes with degree-2 variable nodes [16], [19].…”

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Characterization and efficient exhaustive search algorithm for elementary trapping sets of irregular LDPC codes

Hashemi

Banihashemi

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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In this paper, we propose a characterization of elementary trapping sets (ETSs) for irregular lowdensity parity-check (LDPC) codes. These sets are known to be the main culprits in the error floor region of such codes. The characterization of ETSs for irregular codes has been known to be a challenging problem due to the large variety of non-isomorphic ETS structures that can exist within the Tanner graph of these codes. This is a direct consequence of the variety of the degrees of the variable nodes that can participate in such structures. The proposed characterization is based on a hierarchical graphical representation of ETSs, starting from simple cycles of the graph, or from single variable nodes, and involves three simple expansion techniques: degree-one tree (dot), path and lollipop, thus, the terminology dpl characterization. A similar dpl characterization was proposed in an earlier work by the authors for the leafless ETSs (LETSs) of variable-regular LDPC codes. The present paper generalizes the prior work to codes with a variety of variable node degrees and to ETSs that are not leafless. The proposed dpl characterization corresponds to an efficient search algorithm that, for a given irregular LDPC code, can find all the instances of (a, b) ETSs with size a and with the number of unsatisfied check nodes b within any range of interest a ≤ a max and b ≤ b max , exhaustively. Although, (brute force) exhaustive search algorithms for ETSs of irregular LDPC codes exist, to the best of our knowledge, the proposed search algorithm is the first of its kind, in that, it is devised based on a characterization of ETSs that makes the search process efficient. Extensive simulation results are presented to show the versatility of the search algorithm, and to demonstrate that, compared to the literature, significant improvement in search speed can be obtained.

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Characterization and efficient exhaustive search algorithm for elementary trapping sets of irregular LDPC codes

Hashemi

Banihashemi

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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“…Leafless ETSs (LETSs) are known to be the main problematic structures in the error floor region of variable-regular LDPC codes. For irregular LDPC codes, however, in addition to LETSs, there are other ETSs that are problematic but are not leafless, i.e., they have variable nodes that are connected to only one satisfied check node [62], [1], [47], [53], [76], [23]. This is particularly the case for irregular codes with degree-2 variable nodes [47], [53].…”

Section: Trapping Sets For Irregular Ldpc Codesmentioning

confidence: 99%

Characterization of Problematic Graphical Structures of LDPC Codes and the Corresponding Efficient Search Algorithms

Toroghi¹

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In this thesis, we study all the problematic graphical structures which play important roles in the error floor performance and error correction capability of low-density parity-check (LDPC) codes. These graphical structures are: leafless elementary trapping sets (LETSs), elementary trapping sets (ETSs), non-elementary trapping sets (NETSs), stopping sets and codewords. Recently, Karimi and Banihashemi proposed a characterization of LETSs, which was based on viewing a LETS as a layered superset (LSS) of a short cycle in the code's Tanner graph. However this characterization was not exhaustive. In this work, first, we complement LSS characterization by demonstrating how the remaining structures of LETSs can be characterized. Then, we propose a new characterization for LETSs of variable-regular LDPC codes. Compared to the LSS-based characterization, which is based on a single LSS expansion technique, the new characterization involves two additional expansion techniques. The introduction of the new techniques mitigates the search efficiency problem that LSS-based characterization/search suffers from. We prove that using the three expansion techniques, any LETS structure can be obtained starting from a simple cycle, no matter how large the size of the structure a or the number of its unsatisfied check nodes b are, i.e., the characterization is exhaustive. We also demonstrate that for the proposed characterization/search the length of the short cycles required to be enumerated is minimal. We also prove that the three expansion techniques, proposed here, are the only expansions needed for characterization of LETS structures starting from simple cycles in the graph.Moreover, we generalize the proposed approach of variable-regular to irregular LDPC codes. We explain how the characterization of LETS structures in variableregular graphs can be used to characterize the LETS structures of irregular graphs (in a given range of a and b values, exhaustively). This characterization corresponds to an exhaustive search algorithm. However, this approach is not applicable to irregular LDPC codes, if we are interested to find LETSs in a relatively wide range of iii First, I would like to thank my supervisor, Professor Amir H. Banihashemi for leading and encouraging me during my research. His guidance helped me in all the time of research and writing of this thesis.Thanks must also go to my committee members for their helpful suggestions and discussions.

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Characterization of Elementary Trapping Sets in Irregular LDPC Codes and the Corresponding Efficient Exhaustive Search Algorithms

Hashemi

Banihashemi

2018

IEEE Trans. Inform. Theory

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High Speed Low Error Floor Hardware Implementation and Fast and Accurate Error Floor Estimation of LDPC Decoders

Cited by 3 publications

References 63 publications

Characterization and efficient exhaustive search algorithm for elementary trapping sets of irregular LDPC codes

Characterization and efficient exhaustive search algorithm for elementary trapping sets of irregular LDPC codes

Characterization of Problematic Graphical Structures of LDPC Codes and the Corresponding Efficient Search Algorithms

Characterization of Elementary Trapping Sets in Irregular LDPC Codes and the Corresponding Efficient Exhaustive Search Algorithms

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