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IEEE Communications Letters

Noisy Gradient Descent Bit-Flipping Decoder Based on Adjustment Factor for LDPC Codes

Bin Dai, Rongke Liu, Chenyu Gao, Zhen Mei

Published Apr 9, 2018• 15 citations
Publisher

Abstract

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.

DOI
10.1109/lcomm.2018.2824803

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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.
Gradient descent bit flipping (GDBF) algorithm is an important low-complexity method for decoding LDPC codes. In particular, the multi-bit GDBF decoding has the best decoding performance among BF algorithms if a suitable threshold is prescribed. However, extensive computer searches are needed to find such a threshold for a specific LDPC code. In this paper, we propose a syndrome-aided GDBF (SAGDBF) algorithm to address the problem. The thresholds in our algorithm are adaptively adjusted according to the syndrome values in the iterative process. Simulation results for different LDPC codes suggest that the error performances of the proposed SAGDBF algorithm are close to and even better than the original multi-bit GDBF algorithm at a relatively small number of iterations. In addition, the complexity increased in our proposed algorithm is negligible compared with the original multi-bit GDBF algorithm. Hence, the proposed algorithm is suitable for practical purposes.
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.
Gradient descent bit-flipping (GDBF) algorithm achieves good error performance for decoding low density parity check codes. In the GDBF algorithm, a search point is apt to be trapped in a local optimum, which causes performance degradation of the GDBF algorithm. To overcome this issue, the noisy GDBF algorithm introduces random perturbation into the inversion function of each symbol, which decreases the probability of being trapped in a local optimum. In this paper, we develop the noisy GDBF algorithm by enhancing the threshold adaptation in multi-bit flipping procedure to improve the BER performance without increasing the time complexity.
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.
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.