LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure Analysis [PDF]
EntropyIn this paper, we investigate the cycle structure inherent in the Tanner graphs of low-density parity-check (LDPC) codes constructed from balanced incomplete block designs (BIBDs).
Hengzhou Xu +4 more
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Determining the Upper-Bound on the Code Distance of Quantum Stabilizer Codes Through the Monte Carlo Method Based on Fully Decoupled Belief Propagation [PDF]
EntropyThe code distance is a critical parameter of quantum stabilizer codes (QSCs), and determining it—whether exactly or approximately—is known to be an NP-complete problem.
Zhipeng Liang +4 more
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Adaptive Learned Belief Propagation for Decoding Error-Correcting Codes [PDF]
EntropyWeighted belief propagation (WBP) for the decoding of linear block codes is considered. In WBP, the Tanner graph of the code is unrolled with respect to the iterations of the belief propagation decoder.
Alireza Tasdighi, Mansoor Yousefi
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ON THE CLASS OF ARRAY-BASED APM-LDPC CODES [PDF]
Journal of Algebraic Systems, 2021 We construct an explicit class of affine permutation matrix low-density parity-check (APM-LDPC) codes based on the array parity-check matrix by using two affine maps f (x) = x-1 and g(x) = 2x-1 on Z_m, where m is an odd prime number, with girth 6 and ...
A. Nassaj, A. R. Naghipour
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Quantum message-passing algorithm for optimal and efficient decoding [PDF]
Quantum, 2022 Recently, Renes proposed a quantum algorithm called belief propagation with quantum messages (BPQM) for decoding classical data encoded using a binary linear code with tree Tanner graph that is transmitted over a pure-state CQ channel \cite{renes_2017 ...
Christophe Piveteau, Joseph M. Renes
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A REDUCTION IN THE SEARCH SPACE OF QC-LDPC CODES WITH GIRTH 8 [PDF]
Journal of Algebraic Systems, 2020 In this paper, we define a structure to obtain exponent matrices of girth-8 QC-LDPC codes with column weight 3. Using the difference matrices introduced by Amirzade et al., we investigate necessary and sufficient conditions which result in a Tanner graph
F. Amirzade +2 more
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Efficient Decoding of Turbo Codes with Nonbinary Belief Propagation
EURASIP Journal on Wireless Communications and Networking, 2008 This paper presents a new approach to decode turbo codes using a nonbinary belief propagation decoder. The proposed approach can be decomposed into two main steps.
Thierry Lestable +2 more
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A Neural Network Empowered Belief Propagation Algorithm Optimized for Short-Cycles in Tanner Graph
IEEE Transactions on Machine Learning in Communications and Networking, 2023 Short-cycles in Tanner graphs have a direct impact on the accuracy and effectiveness of the belief propagation (BP) algorithm, as they diverge the BP algorithm by disrupting the independency of message transmission.
Hao Xu, Ying Li, Bin Tan, Jun Wu, Die Hu
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A Note on the Girth of (3, 19)-Regular Tanner’s Quasi-Cyclic LDPC Codes
IEEE Access, 2021 In this article, we study the cycle structure of (3, 19)-regular Tanner’s quasi-cyclic (QC) LDPC codes with code length $19p$ , where $p$ is a prime and $p\equiv 1~(\bmod ~57)$ , and transform the conditions for the existence of cycles of ...
Manjie Zhou +4 more
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Effective identification of dominant fully absorbing sets for Raptor-like LDPC codes
ETRI Journal, 2023 The error-rate floor of low-density parity-check (LDPC) codes is attributed to the trapping sets of their Tanner graphs. Among them, fully absorbing sets dominantly affect the error-rate performance, especially for short blocklengths.
Woncheol Cho +3 more
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