Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Access

Offset Gradient Descent Bit-Flipping Decoding for Irregular Parity-Check Codes

Woohong Min, Kyeongcheol Yang

Published Jan 1, 2026• 0 citations
Publisher

Abstract

A key challenge for decoding irregular parity-check codes under the gradient descent bit-flipping (GDBF) algorithm is that the irregularity in column degrees reduces the accuracy of the reliability measurements obtained through a flipping function (FF). To address the challenge, we introduce a novel approach based on the gradient descent bit-flipping with momentum (GDBF-w/M). We first propose an offset GDBF-w/M (OGDBF-w/M) algorithm for decoding column-irregular codes over the additive white Gaussian noise channel, where the FF includes an offset term depending on column degrees.We then propose a diversity-based offset GDBF-w/M (D-OGDBF-w/M) algorithm which employs multiple OGDBF-w/M decoders with distinct offset values. Furthermore, we extend the proposed algorithms to the binary symmetric channel, although they are initially intended for the additive white Gaussian noise channel. Numerical results demonstrate that they achieve significant improvements in decoding performance for irregular parity-check codes, particularly for column-irregular codes.

DOI
10.1109/access.2026.3679598

Related papers

Noisy Gradient Descent Bit-Flip Decoding for LDPC Codes

Gopalakrishnan Sundararajan, Chris Winstead, Emmanuel Boutillon

A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes on the binary-input additive white Gaussian noise channel. The new algorithm, called Noisy GDBF (NGDBF), introduces a random perturbation into each symbol metric at each iteration. The noise perturbation allows the algorithm to escape from undesirable local maxima, resulting in improved performance. A combination of heuristic improvements to the algorithm are proposed and evaluated. When the proposed heuristics are applied, NGDBF performs better than any previously reported GDBF variant, and comes within 0.5 dB of the belief propagation algorithm for several tested codes. Unlike other previous GDBF algorithms that provide an escape from local maxima, the proposed algorithm uses only local, fully parallelizable operations and does not require computing a global objective function or a sort over symbol metrics, making it highly efficient in comparison. The proposed NGDBF algorithm requires channel state information which must be obtained from a signal to noise ratio (SNR) estimator. Architectural details are presented for implementing the NGDBF algorithm. Complexity analysis and optimizations are also discussed.

arXiv:1402.2773•IEEE Transactions on Communications•Sep 9, 2014•108 citations

Channel-Aware Gradient Descent Bit-Flipping Algorithm for LDPC Codes

Woohong Min, Kyeongcheol Yang

The gradient descent bit-flipping with momentum (GDBF-w/M) and probabilistic GDBF-w/M (PGDBF-w/M) algorithms significantly improve the decoding performance of the bit-flipping (BF) algorithm. In this letter, we propose a channel-aware GDBF-w/M algorithm which operates deterministically based on the received values from the additive white Gaussian noise (AWGN) channel. Numerical results show that the proposed algorithm does not only mitigate the error-floor phenomenon of the GDBF-w/M algorithm, but it also has better decoding performance than the PGDBF-w/M algorithm without the need for a random number generator. Furthermore, the complexity of the proposed algorithm is slightly higher than that of the GDBF-w/M algorithm.

IEEE Communications Letters•Feb 20, 2025•3 citations

Efficient Bit-Flipping Decoding Algorithm for Structured LDPC Codes

Cheng He, Yuzhu Wang

The Gradient descent bit flipping (GDBF) algorithm is a representative approach for decoding low-density parity-check (LDPC) codes, which offers a good tradeoff between decoding performance and complexity. Unfortunately, the decoding performance of GDBF algorithm degenerates dramatically for structured LDPC codes due to their large column weight. To address the above issue, we propose to improve GDBF algorithm by introducing a weighted parameter in the energy function of each bit. Specifically, this parameter compensates for the computational error of the energy function due to the large column weight of the parity-check matrices of structured LDPC codes. Moreover, the flipping number of each bit in the iterative process is included in the energy function to avoid consecutive bit flips in the decoding. Simulation results on typical structured LDPC codes indicate that the performance of the proposed algorithm is better than the standard GDBF algorithm at the cost of slight increment in the algorithmic complexity. The increase operations can be easily implemented, which indicates the proposed algorithm is suitable for practical purposes.

International Conference on Neural Networks, Information and Communication Engineering (NNICE)•Jan 10, 2025•0 citations

Improved noisy gradient descent bit-flipping algorithm over Rayleigh fading channel

Reza Biazaran, Hermann J. Helgert

Gradient descent bit flipping (GDBF) and its many variants have offered remarkable improvements over legacy, or modified, bit flipping decoding techniques in case of decoding low density parity check (LDPC) codes. GDBF method and its many variants, such as noisy gradient descent bit flipping (NGDBF) have been extensively studied and their performances have been assessed over multiple channels such as binary symmetric channel (BSC), binary erasure channel (BEC) and additive white Gaussian noise (AWGN) channel. However, performance of the said decoders in more realistic channels or channel conditions have not been equally studied. An improved noisy gradient descent bit flipping algorithm is proposed in this paper that optimally decodes LDPC encoded codewords over Rayleigh fading channel and under various fade rates. Comparing to NGDBF method, our proposed decoder provides substantial improvements in both error performance of the code, and in the number of iterations required to achieve the said error performance. It subsequently reduces the end-to-end latency in applications with low or ultra-low latency requirements.

International Journal of Power Electronics and Drive Systems/International Journal of Electrical and Computer Engineering•Mar 14, 2022•3 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.

IEEE Computer Society Annual Symposium on VLSI•Jun 20, 2023•3 citations

Multi-bit flip type gradient descent bit flipping decoding using no thresholds

Ryoji Haga, Shogo Usami

Gradient Descent Bit Flipping (GDBF) decoding has one of the best decoding performances of the bit flip type decoding algorithms for low density parity check code. Multi-bit type GDBF decoding, however, achieves good error performance only with suitable thresholds. In this paper, we propose multi-bit type GDBF decoding without using thresholds. The proposed method estimates the number of bits to flip from the received soft sequence using the characteristic of the probability density distribution of the additive white Gaussian noise channel. The error performance of the proposed method is almost equal to that of the conventional method despite not using thresholds.

International Symposium on Information Theory and its Applications•Oct 1, 2012•4 citations
A key challenge for decoding irregular parity-check codes under the gradient descent bit-flipping (GDBF) algorithm is that the irregularity in column degrees reduces the accuracy of the reliability measurements obtained through a flipping function (FF). To address the challenge, we introduce a novel approach based on the gradient descent bit-flipping with momentum (GDBF-w/M). We first propose an offset GDBF-w/M (OGDBF-w/M) algorithm for decoding column-irregular codes over the additive white Gaussian noise channel, where the FF includes an offset term depending on column degrees.We then propose a diversity-based offset GDBF-w/M (D-OGDBF-w/M) algorithm which employs multiple OGDBF-w/M decoders with distinct offset values. Furthermore, we extend the proposed algorithms to the binary symmetric channel, although they are initially intended for the additive white Gaussian noise channel. Numerical results demonstrate that they achieve significant improvements in decoding performance for irregular parity-check codes, particularly for column-irregular codes.
A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes on the binary-input additive white Gaussian noise channel. The new algorithm, called Noisy GDBF (NGDBF), introduces a random perturbation into each symbol metric at each iteration. The noise perturbation allows the algorithm to escape from undesirable local maxima, resulting in improved performance. A combination of heuristic improvements to the algorithm are proposed and evaluated. When the proposed heuristics are applied, NGDBF performs better than any previously reported GDBF variant, and comes within 0.5 dB of the belief propagation algorithm for several tested codes. Unlike other previous GDBF algorithms that provide an escape from local maxima, the proposed algorithm uses only local, fully parallelizable operations and does not require computing a global objective function or a sort over symbol metrics, making it highly efficient in comparison. The proposed NGDBF algorithm requires channel state information which must be obtained from a signal to noise ratio (SNR) estimator. Architectural details are presented for implementing the NGDBF algorithm. Complexity analysis and optimizations are also discussed.
The gradient descent bit-flipping with momentum (GDBF-w/M) and probabilistic GDBF-w/M (PGDBF-w/M) algorithms significantly improve the decoding performance of the bit-flipping (BF) algorithm. In this letter, we propose a channel-aware GDBF-w/M algorithm which operates deterministically based on the received values from the additive white Gaussian noise (AWGN) channel. Numerical results show that the proposed algorithm does not only mitigate the error-floor phenomenon of the GDBF-w/M algorithm, but it also has better decoding performance than the PGDBF-w/M algorithm without the need for a random number generator. Furthermore, the complexity of the proposed algorithm is slightly higher than that of the GDBF-w/M algorithm.
The Gradient descent bit flipping (GDBF) algorithm is a representative approach for decoding low-density parity-check (LDPC) codes, which offers a good tradeoff between decoding performance and complexity. Unfortunately, the decoding performance of GDBF algorithm degenerates dramatically for structured LDPC codes due to their large column weight. To address the above issue, we propose to improve GDBF algorithm by introducing a weighted parameter in the energy function of each bit. Specifically, this parameter compensates for the computational error of the energy function due to the large column weight of the parity-check matrices of structured LDPC codes. Moreover, the flipping number of each bit in the iterative process is included in the energy function to avoid consecutive bit flips in the decoding. Simulation results on typical structured LDPC codes indicate that the performance of the proposed algorithm is better than the standard GDBF algorithm at the cost of slight increment in the algorithmic complexity. The increase operations can be easily implemented, which indicates the proposed algorithm is suitable for practical purposes.
Gradient descent bit flipping (GDBF) and its many variants have offered remarkable improvements over legacy, or modified, bit flipping decoding techniques in case of decoding low density parity check (LDPC) codes. GDBF method and its many variants, such as noisy gradient descent bit flipping (NGDBF) have been extensively studied and their performances have been assessed over multiple channels such as binary symmetric channel (BSC), binary erasure channel (BEC) and additive white Gaussian noise (AWGN) channel. However, performance of the said decoders in more realistic channels or channel conditions have not been equally studied. An improved noisy gradient descent bit flipping algorithm is proposed in this paper that optimally decodes LDPC encoded codewords over Rayleigh fading channel and under various fade rates. Comparing to NGDBF method, our proposed decoder provides substantial improvements in both error performance of the code, and in the number of iterations required to achieve the said error performance. It subsequently reduces the end-to-end latency in applications with low or ultra-low latency requirements.
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.
Gradient Descent Bit Flipping (GDBF) decoding has one of the best decoding performances of the bit flip type decoding algorithms for low density parity check code. Multi-bit type GDBF decoding, however, achieves good error performance only with suitable thresholds. In this paper, we propose multi-bit type GDBF decoding without using thresholds. The proposed method estimates the number of bits to flip from the received soft sequence using the characteristic of the probability density distribution of the additive white Gaussian noise channel. The error performance of the proposed method is almost equal to that of the conventional method despite not using thresholds.