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Error Correction Capability of LDPC Codes Under the Bit-Flipping Decoding Algorithm

Hiroto Tamiya, Masanori Hirotomo, Masakatu Morii

IEICE Technical Report; IEICE Tech. Rep.Jul 6, 20151 citation

On error correction capability of bit-flipping algorithm for LDPC codes

Wen-Yao Chen, Chung-Chin Lu

The error correction capability of bit-flipping decoding algorithm for low density parity-check (LDPC) codes is studied by introducing variable node adjacency (VNA) graphs which are derived from Tanner graphs of LDPC codes. For codes with column weight λ and girth g = 8, it can be shown that error patterns of weight less than or equal to λ - 1 can be corrected. This result implies that the bit-flipping algorithm could decode up to the random error-correcting capability over binary symmetric channel for girth 8 codes whose random error-correcting capability is equal to λ - 1.The error correction capability of bit-flipping decoding algorithm for low density parity-check (LDPC) codes is studied by introducing variable node adjacency (VNA) graphs which are derived from Tanner graphs of LDPC codes. For codes with column weight λ and girth g = 8, it can be shown that error patterns of weight less than or equal to λ - 1 can be corrected. This result implies that the bit-flipping algorithm could decode up to the random error-correcting capability over binary symmetric channel for girth 8 codes whose random error-correcting capability is equal to λ - 1.

IEEE International Symposium on Information Theory (ISIT)Jul 1, 20116 citations

Reliability-Based Single Bit-Flipping Decoding Algorithm for LDPC Codes

Soufian Addi, Mostafa Belkasmi, Ahlam Berkani +1 more

Lecture notes in electrical engineeringJan 1, 20240 citations

Column-Weighted Probabilistic GDBF Decoder for Irregular LDPC Codes

Changfu He, Keyue Deng, Suwen Song +1 more

Existing bit-flipping algorithms, when used for irregular low-density parity-check (LDPC) codes, often suffer from performance degradation due to the imbalance caused by the irregular codeword structure. To alleviate this problem, this paper presents a column-weighted probabilistic gradient-descent bit-flipping (CW-PGDBF) decoder for irregular LDPC codes. Different weighting factors are allocated to variable nodes with different column weights to solve the imbalance. Furthermore, a modified probabilistic flipping rule is employed to reduce the hardware complexity while maintaining the error-correction performance. Simulation results demonstrate that the proposed algorithm can achieve significantly improved performance compared with other BF-based algorithms for irregular codes. Additionally, a hardware architecture for the CW-PGDBF decoder is proposed with acceptable hardware overhead compared to the original PGDBF decoder.Existing bit-flipping algorithms, when used for irregular low-density parity-check (LDPC) codes, often suffer from performance degradation due to the imbalance caused by the irregular codeword structure. To alleviate this problem, this paper presents a column-weighted probabilistic gradient-descent bit-flipping (CW-PGDBF) decoder for irregular LDPC codes. Different weighting factors are allocated to variable nodes with different column weights to solve the imbalance. Furthermore, a modified probabilistic flipping rule is employed to reduce the hardware complexity while maintaining the error-correction performance. Simulation results demonstrate that the proposed algorithm can achieve significantly improved performance compared with other BF-based algorithms for irregular codes. Additionally, a hardware architecture for the CW-PGDBF decoder is proposed with acceptable hardware overhead compared to the original PGDBF decoder.

IEEE Computer Society Annual Symposium on VLSIJun 20, 20233 citations

Adaptive Sub-Optimal Bit Flipping Decoding Algorithm for LDPC

S. Ashwin Kumar, R. Aravinthan, Ch. Sriram Reddy +2 more

Lecture notes on data engineering and communications technologiesJan 1, 20210 citations

Error correction capability of irregular LDPC codes under the Gallager a algorithm

Masakatu Morii, Hiroto Tamiya, Masanori Hirotomo

Many researchers have analyzed the error correction capability of LDPC codes for iterative decoding algorithms. However, it is difficult to show the error correction capability of LDPC codes for iterative decoding algorithms based on belief propagation theoretically. Chilappagari et al. reported the error correction capability of column-weight-three regular LDPC codes under the Gallager A algorithm since the behavior of the iterative decoding algorithm is easily analyzed. In this paper, we investigate the error correction capability of irregular LDPC codes. We also show relations between the decoding failures and 2-cycles of irregular LDPC codes under the Gallager A algorithm.Many researchers have analyzed the error correction capability of LDPC codes for iterative decoding algorithms. However, it is difficult to show the error correction capability of LDPC codes for iterative decoding algorithms based on belief propagation theoretically. Chilappagari et al. reported the error correction capability of column-weight-three regular LDPC codes under the Gallager A algorithm since the behavior of the iterative decoding algorithm is easily analyzed. In this paper, we investigate the error correction capability of irregular LDPC codes. We also show relations between the decoding failures and 2-cycles of irregular LDPC codes under the Gallager A algorithm.

International Symposium on Information Theory and its ApplicationsOct 1, 20162 citations

On Error Correction Capability of Irregular LDPC Codes under the Bit-Flipping Decoding Algorithm

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