A fast reconstruction of the parity-check matrices of LDPC codes in a noisy environment

Liu, Qian; Zhang, Hao; Gao-feng, Shen; Mei, Fengtong

doi:10.1016/j.comcom.2021.05.023

Cited by 3 publications

(33 citation statements)

References 14 publications

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“…From [20] we know, we can derive all the parity-checks through implying Gauss column elimination on the error-free codeword matrix. Based on this fact and the above conclusion, Authors in [18][19][20] obtain parity-checks by searching low weight columns (dependent columns) from the noisy codeword matrix after Gauss column elimination.…”

Section: The Algorithms Based On Gauss Column Eliminationmentioning

confidence: 99%

“…The method proposed in [19] introduced a decoding technique approach to speed up the process of acquiring parity-checks based on the work in [18]. For the reconstruction of the parity-check matrices of LDPC codes, an algorithm [20] was proposed. Which needed much less iterations compared with [19] for using a technique BGCE (Bidirectional Gaussian Column Elimination).…”

Section: Introductionmentioning

confidence: 99%

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A Two-Step Screening Algorithm to Solve Linear Error Equations for Blind Identification of Block Codes Based on Binary Galois Field

Liu¹,

Zhang²,

Yu³

et al. 2021

KSII TIIS

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Existing methods for blind identification of linear block codes without a candidate set are mainly built on the Gauss elimination process. However, the fault tolerance will fall short when the intercepted bit error rate (BER) is too high. To address this issue, we apply the reverse algebra approach and propose a novel "two-step-screening" algorithm by solving the linear error equations on the binary Galois field, or GF(2). In the first step, a recursive matrix partition is implemented to solve the system linear error equations where the coefficient matrix is constructed by the full codewords which come from the intercepted noisy bitstream. This process is repeated to derive all those possible parity-checks. In the second step, a check matrix constructed by the intercepted codewords is applied to find the correct parity-checks out of all possible parity-checks solutions. This novel "two-step-screening" algorithm can be used in different codes like Hamming codes, BCH codes, LDPC codes, and quasi-cyclic LDPC codes. The simulation results have shown that it can highly improve the fault tolerance ability compared to the existing Gauss elimination process-based algorithms.

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Section: The Algorithms Based On Gauss Column Eliminationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Two-Step Screening Algorithm to Solve Linear Error Equations for Blind Identification of Block Codes Based on Binary Galois Field

Liu¹,

Zhang²,

Yu³

et al. 2021

KSII TIIS

View full text Add to dashboard Cite

show abstract

“…To further improve the fault tolerance performance, an optimal threshold was proposed to sort the code words and a bi-directional Gaussian column elimination (BGCE) operation was proposed to speed up the process of deriving the parity-checks in ref. [19]. The method in ref.…”

Section: Introductionmentioning

confidence: 99%

“…The method in ref. [19] mainly improves the first step of the method in ref. [18] by exploiting the reliability of the intercepted signal.…”

Section: Introductionmentioning

confidence: 99%

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Blind recognition of sparse parity‐check matrices of low‐density parity‐check codes in the presence of noise

2022

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This paper studies the blind recognition method of the sparse parity‐check matrices of low‐density parity‐check codes in noncooperative communication, which is critical to the reverse analysis of communication protocols using LDPC codes. In this paper, two improvements are made to the algorithm of Liu Qian et al. (2021) for this problem. Firstly, a Gaussian elimination method based on random column exchange and soft information is proposed to enhance the fault tolerance of the elimination process. Secondly, according to the sparse property of the parity‐check matrices of LDPC codes, a random extraction method is proposed to further improve the fault tolerance of the algorithm, and it is verified theoretically. Finally, simulations verify the superior performance of the algorithm proposed in this paper.

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Joint blind reconstruction of cyclic codes and self‐synchronous scramblers

2023

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The inverse analysis of the intercepted signals to reconstruct the communication scheme used by the transmitter is a key problem in the non‐cooperative context. In this paper, the problem of blind reconstruction of cyclic codes and self‐synchronous scramblers is considered. There is no existing solution to this problem. To solve this problem, a joint blind reconstruction method for cyclic codes and self‐synchronous scramblers is proposed in this paper. A lemma is proposed and proved theoretically that the maximum common factor of the inverse polynomial of the polynomial form of the dual vectors of the self‐synchronous scrambled bit matrix is the product of the parity polynomial of the cyclic code and the feedback polynomial of the self‐synchronous scrambler. Using this lemma, the joint blind reconstruction of the cyclic code and the self‐synchronous scrambler is completed. Finally, a Gaussian elimination based on random column exchange and soft information (GERCESI) method is proposed, which can apply the proposed method to a noisy environment. Simulations prove that the fault‐tolerance performance of the GERCESI method proposed in this paper is at least 0.5 dB higher than that of the GJETP method.

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A fast reconstruction of the parity-check matrices of LDPC codes in a noisy environment

Cited by 3 publications

References 14 publications

A Two-Step Screening Algorithm to Solve Linear Error Equations for Blind Identification of Block Codes Based on Binary Galois Field

A Two-Step Screening Algorithm to Solve Linear Error Equations for Blind Identification of Block Codes Based on Binary Galois Field

Blind recognition of sparse parity‐check matrices of low‐density parity‐check codes in the presence of noise

Joint blind reconstruction of cyclic codes and self‐synchronous scramblers

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