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

Error-Floors of the 802.3an LDPC Code for Noise Assisted Decoding

Tasnuva Tithi

Published May 8, 2019• 0 citations
Publisher

Abstract

In digital communication, information is sent as bits, which is corrupted by the noise present in wired/wireless medium known as the channel. The Low Density Parity Check (LDPC) codes are a family of error correction codes used in communication systems to detect and correct erroneous data at the receiver. Data is encoded with error correction coding at the transmitter and decoded at the receiver. The Noisy Gradient Descent BitFlip (NGDBF) decoding algorithm is a new algorithm with excellent decoding performance with relatively low implementation requirements. This dissertation aims to characterize the performance of the NGDBF algorithm. A simple improvement over NGDBF called the Re-decoded NGDBF (R-NGDBF) is proposed to enhance the performance of NGDBF decoding algorithm. A general method to estimate the decoding parameters of NGDBF is presented. The estimated parameters are then verified in a hardware implementation of the decoder to validate the accuracy of the estimation technique.

DOI
10.26076/kvmz-tz82

Related papers

Decoding LDPC codes via Noisy Gradient Descent Bit-Flipping with Re-Decoding

Tasnuva Tithi, Chris Winstead, Gopalakrishnan Sundararajan

In this paper, we consider the performance of the Noisy Gradient Descent Bit Flipping (NGDBF) algorithm under re-decoding of failed frames. NGDBF is a recent algorithm that uses a non-deterministic gradient descent search to decode low-density parity check (LDPC) codes. The proposed re-decode procedure obtains improved performance because the perturbations are independent at each re-decoding phase, therefore increasing the likelihood of successful decoding. We examine the benefits of re-decoding for an LDPC code from the IEEE 802.3an standard, and find that only a small fraction of re-decoded frames are needed to obtain significant performance benefits. When re-decoding is used, the NGDBF performance is very close to a benchmark offset min-sum decoder for the 802.3an code.

arXiv:1503.08913•Mar 31, 2015•6 citations

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

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

Gradient-Descent Bit-Flipping Decoding Based on Tabu Search for LDPC Codes

良介 高橋, 祐一 高野

This paper is concerned with bit-flipping algorithms for decoding low-density parity check codes. The gradient-descent bit flipping (GDBF) is known as a high-performance class of bitflipping algorithms; however, once GDBF becomes trapped at local optimal solutions, it cannot escape from them. Several algorithms, including noisy gradient-descent bit flipping (NGDBF), have been devised to overcome this drawback. For the same purpose, we develop a bit-flipping algorithm based on the tabu search, which is one of the most effective metaheuristics. The simulation results demonstrate that our algorithm achieved higher bit error rate performance than GDBF did. Moreover, our algorithm required a smaller number of iterations to find a good-quality solution than NGDBF did.

•Mar 1, 2019•0 citations

Hardware Implementation of Modified Noisy Gradient Descent Bit-Flipping Decoders

Qingan Li, Wai-Man Tam, Francis C. M. Lau

Recently, modified noisy gradient descent bit flipping (MNGDBF) algorithms have been proposed to eliminate the Gaussian random generators required in the original noisy gradient descent bit flipping (NGDBF) algorithm for the decoding of low-density parity-check (LDPC) codes. In this paper, a platform has been established for the hardware implementation of the LDPC encoder, the Gaussian noise channel generator and the decoder using MNGDBF decoding algorithms based on the use of field programmable gate array (FPGA). With 6-bit quantization, results show that the error performance achieved by hardware experiments is similar to that obtained by floating-point computer simulations. Moreover, we propose a new MNGDBF algorithm, in which the flipping condition is determined with the help of the summation of all inversion functions. Experimental results show that the proposed algorithm has superior performance than the original MNGDBF algorithm.

IEEE International Symposium on Circuits and Systems proceedings•May 25, 2025•1 citation

Tabu-List Noisy Gradient Descent Bit Flipping Decoding of LDPC Codes

Li Guo Zhang, Nan Liu, Zhiwen Pan +1 more

The Noisy Gradient Descent Bit Flipping (NGDBF) algorithm surpasses the previous Gradient Descent Bit Flipping (GDBF) and other Bit Flipping (BF) algorithms for decoding Low-Density Parity-Check (LDPC) codes. However, the NGDBF decoder sometimes cannot escape from the local maxima. To further enhance the performance of the NGDBF algorithm, an improved NGDBF algorithm called Tabu-List Noisy Gradient Descent Bit Flipping (TNGDBF) is proposed in this paper. A tabu-list is employed to help the NGDBF decoder escape from the local maxima. It is shown in the simulation results that the TNGDBF algorithm gains about 0.2 dB performance compared with NGDBF at the cost of a small amount of complexity increase.

International Conference on Wireless Communications and Signal Processing (WCSP)•Oct 1, 2019•2 citations
In digital communication, information is sent as bits, which is corrupted by the noise present in wired/wireless medium known as the channel. The Low Density Parity Check (LDPC) codes are a family of error correction codes used in communication systems to detect and correct erroneous data at the receiver. Data is encoded with error correction coding at the transmitter and decoded at the receiver. The Noisy Gradient Descent BitFlip (NGDBF) decoding algorithm is a new algorithm with excellent decoding performance with relatively low implementation requirements. This dissertation aims to characterize the performance of the NGDBF algorithm. A simple improvement over NGDBF called the Re-decoded NGDBF (R-NGDBF) is proposed to enhance the performance of NGDBF decoding algorithm. A general method to estimate the decoding parameters of NGDBF is presented. The estimated parameters are then verified in a hardware implementation of the decoder to validate the accuracy of the estimation technique.
In this paper, we consider the performance of the Noisy Gradient Descent Bit Flipping (NGDBF) algorithm under re-decoding of failed frames. NGDBF is a recent algorithm that uses a non-deterministic gradient descent search to decode low-density parity check (LDPC) codes. The proposed re-decode procedure obtains improved performance because the perturbations are independent at each re-decoding phase, therefore increasing the likelihood of successful decoding. We examine the benefits of re-decoding for an LDPC code from the IEEE 802.3an standard, and find that only a small fraction of re-decoded frames are needed to obtain significant performance benefits. When re-decoding is used, the NGDBF performance is very close to a benchmark offset min-sum decoder for the 802.3an code.
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.
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.
This paper is concerned with bit-flipping algorithms for decoding low-density parity check codes. The gradient-descent bit flipping (GDBF) is known as a high-performance class of bitflipping algorithms; however, once GDBF becomes trapped at local optimal solutions, it cannot escape from them. Several algorithms, including noisy gradient-descent bit flipping (NGDBF), have been devised to overcome this drawback. For the same purpose, we develop a bit-flipping algorithm based on the tabu search, which is one of the most effective metaheuristics. The simulation results demonstrate that our algorithm achieved higher bit error rate performance than GDBF did. Moreover, our algorithm required a smaller number of iterations to find a good-quality solution than NGDBF did.
Recently, modified noisy gradient descent bit flipping (MNGDBF) algorithms have been proposed to eliminate the Gaussian random generators required in the original noisy gradient descent bit flipping (NGDBF) algorithm for the decoding of low-density parity-check (LDPC) codes. In this paper, a platform has been established for the hardware implementation of the LDPC encoder, the Gaussian noise channel generator and the decoder using MNGDBF decoding algorithms based on the use of field programmable gate array (FPGA). With 6-bit quantization, results show that the error performance achieved by hardware experiments is similar to that obtained by floating-point computer simulations. Moreover, we propose a new MNGDBF algorithm, in which the flipping condition is determined with the help of the summation of all inversion functions. Experimental results show that the proposed algorithm has superior performance than the original MNGDBF algorithm.
The Noisy Gradient Descent Bit Flipping (NGDBF) algorithm surpasses the previous Gradient Descent Bit Flipping (GDBF) and other Bit Flipping (BF) algorithms for decoding Low-Density Parity-Check (LDPC) codes. However, the NGDBF decoder sometimes cannot escape from the local maxima. To further enhance the performance of the NGDBF algorithm, an improved NGDBF algorithm called Tabu-List Noisy Gradient Descent Bit Flipping (TNGDBF) is proposed in this paper. A tabu-list is employed to help the NGDBF decoder escape from the local maxima. It is shown in the simulation results that the TNGDBF algorithm gains about 0.2 dB performance compared with NGDBF at the cost of a small amount of complexity increase.