Efficient Search of Girth-Optimal QC-LDPC Codes

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

doi:10.1109/tit.2016.2523979

Cited by 68 publications

(85 citation statements)

References 8 publications

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“…Moreover, isomorphism theory of QC LDPC codes was proposed in [39][40][41] based on the isomorphism of graphs in graph theory. According to the isomorphism of QC LDPC codes, the parity-check matrix in (6) can be simplified as the following matrix:…”

Section: Qc Ldpc Codes and Their Associated Tanner Graphsmentioning

confidence: 99%

“…in the exponent matrix P. Furthermore, short cycles of QC LDPC codes can be determined by the elements of P [39,40]. Let be the girth of the code C. It can be seen from [43] that, for ≤ 2 ≤ 2 −2, the necessary and sufficient condition for the existence of a 2 -cycle in the Tanner graph of the code C (or H) can be generalized as follows:…”

Section: Cycle Structure Of Qc Ldpc Codesmentioning

confidence: 99%

“…A visual representation is depicted in Figure 2. Therefore, (4) in [29] and (3) in [39] are not applicable to the cycles with lengths larger than 2 − 2.…”

Section: Cycle Structure Of Qc Ldpc Codesmentioning

confidence: 99%

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Construction of Quasi‐Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

Zhu

et al. 2018

Wireless Communications and Mobile Computing

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Quasi-cyclic (QC) LDPC codes play an important role in 5G communications and have been chosen as the standard codes for 5G enhanced mobile broadband (eMBB) data channel. In this paper, we study the construction of QC LDPC codes based on an arbitrary given expansion factor (or lifting degree). First, we analyze the cycle structure of QC LDPC codes and give the necessary and sufficient condition for the existence of short cycles. Based on the fundamental theorem of arithmetic in number theory, we divide the integer factorization into three cases and present three classes of QC LDPC codes accordingly. Furthermore, a general construction method of QC LDPC codes with girth of at least 6 is proposed. Numerical results show that the constructed QC LDPC codes perform well over the AWGN channel when decoded with the iterative algorithms.

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Section: Qc Ldpc Codes and Their Associated Tanner Graphsmentioning

confidence: 99%

Section: Cycle Structure Of Qc Ldpc Codesmentioning

confidence: 99%

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Construction of Quasi‐Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

Zhu

et al. 2018

Wireless Communications and Mobile Computing

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“…This implies that all the nodes in U ′ have the same degree d v = m and all the nodes in W ′ have the same degree d c = n. Parameters d v and d c are the variable and check node degrees of the constructed regular QC-LDPC code. It is well-known that for any QC-LDPC code with a fully-connected base graph, there exists an isomorphic QC-LDPC code with the exponent matrix June 18, 2019 DRAFT in the following form (see, e.g., [18]):…”

mentioning

confidence: 99%

“…Given the exponent matrix of a QC-LDPC code, the necessary and sufficient condition for having a 2l-cycle in the Tanner graph is [18], [19]:…”

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confidence: 99%

Construction of QC LDPC Codes With Low Error Floor by Efficient Systematic Search and Elimination of Trapping Sets

Karimi

Banihashemi

2020

IEEE Trans. Commun.

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We propose a systematic design of protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes with low error floor. We first characterize the trapping sets of such codes and demonstrate that the QC structure of the code eliminates some of the trapping set structures that can exist in a code with the same degree distribution and girth but lacking the QC structure. Using this characterization, our design aims at eliminating a targeted collection of trapping sets. Considering the parent/child relationship between the trapping sets in the collection, we search for and eliminate those trapping sets that are in the collection but are not a child of any other trapping set in the collection. An efficient layered algorithm is designed for the search of these targeted trapping sets. Compared to the existing codes in the literature, the designed codes are superior in the sense that they are free of the same collection of trapping sets while having a smaller block length, or a larger collection of trapping sets while having the same block length. In addition, the efficiency of the search algorithm makes it possible to design codes with larger degrees which are free of trapping sets within larger ranges compared to the state-of-the-art.

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Construction of Quasi-Cyclic LDPC Codes with Diagonal Structure of Parity-Check Matrices

Zhu

et al. 2018

Communications and Networking

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Efficient Search of Girth-Optimal QC-LDPC Codes

Cited by 68 publications

References 8 publications

Construction of Quasi‐Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

Construction of Quasi‐Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

Construction of QC LDPC Codes With Low Error Floor by Efficient Systematic Search and Elimination of Trapping Sets

Construction of Quasi-Cyclic LDPC Codes with Diagonal Structure of Parity-Check Matrices

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