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IEEE International Symposium on Circuits and Systems proceedings

Hardware Implementation of Modified Noisy Gradient Descent Bit-Flipping Decoders

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

Published May 25, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1109/iscas56072.2025.11043621

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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.
In this paper, we propose modified multi-bit noisy gradient descent bit flipping (M-NGDBF) algorithms for decoding low-density parity-check codes. To simplify the decoder design, we eliminate the use of Gaussian noise generators at the decoder and replace them with received signals after simple transformations. We then improve the convergence rate by removing the randomness in the M-NGDBF algorithm during the first few iterations. Subsequently, we construct a tabu-list to record bits that are flipped in the current iteration and allows these bits to be flipped in the next iteration only with a very small probability. Simulation results show that our proposed algorithms outperform the original M-NGDBF algorithm in terms of both bit error rate and convergence rate.
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.
In this paper, we propose an efficient noisy gradient descent bit-flipping (NGDBF) algorithm for decoding LDPC codes. The proposed algorithm introduces random noise with uniform distribution on the interval[−1,1][-1,1][−1,1]into the inversion function of the GDBF algorithm. The proposed algorithm avoids the complicated operations in the noise generation of the conventional NGDBF algorithm. In addition, our proposed decoding algorithm does not rely on the SNR estimation and the scaling factor. Simulation results indicate that the proposed algorithm can achieve almost the same performance as the conventional NGDBF algorithm. Moreover, even the using of a linear feedback shift register with very small stage can generate sufficient randomness to reach such performance.
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.
As a class of bit-flipping (BF) decoder, the noisy gradient descent bit flipping (NGDBF) algorithm outperforms the original GDBF and other BF algorithms. To increase the reliability of the inversion function, we propose a modified NGDBF algorithm by introducing an adjustment factor on the syndrome. Moreover, for the multi-bit flipping, we present an adaptive inversion threshold which depends on the numbers of negative bipolar syndromes. The simulation results show that our proposed algorithm outperforms the NGDBF algorithm for both single-bit and multi-bit flipping schemes.