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arXiv:2204.02359 · International Symposium on Turbo Codes and Iterative Information Processing

Gradient Descent Bit-Flipping Decoding with Momentum

Valentin Savin

Published Aug 30, 2021• 23 citations
arXivHTMLPDF

Abstract

In this paper, we propose a Gradient Descent Bit-Flipping (GDBF) decoding with momentum, which considers past updates to provide inertia to the decoding process. We show that GDBF or randomized GDBF decoders with momentum may closely approach the floating-point Belief-Propagation decoding performance, and even outperform it in the error-floor region, especially for graphs with high connectivity degree.

DOI
10.1109/istc49272.2021.9594128

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arXiv:1402.2773•IEEE Transactions on Communications•Sep 9, 2014•108 citations
In this paper, we propose a Gradient Descent Bit-Flipping (GDBF) decoding with momentum, which considers past updates to provide inertia to the decoding process. We show that GDBF or randomized GDBF decoders with momentum may closely approach the floating-point Belief-Propagation decoding performance, and even outperform it in the error-floor region, especially for graphs with high connectivity degree.
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.
Gradient descent bit-flipping (GDBF) decoding for low-density parity-check (LDPC) codes has gained great attentions because of low complexity and relatively good performance. However, the performance of the GDBF decoding is still much poorer than that of the MS algorithm. To further improve the performance, the iterative decoding process is introduced to GDBF decoding in this paper. At the end of each iteration, the latest information is used to update the reliability of the flipped bit, by which its reliability is greatly improved. Simulation results indicate that the proposed algorithm has about 0.4 dB performance gains compared to GDBF. Meanwhile, there is small computational complexity increased.
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 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.
In this letter we propose a novel framework for designing decoders, for Low-Density Parity Check (LDPC) codes, that surpasses the frame error rate performance of Belief-Propagation (BP) decoding on binary symmetric channels. Its key component is the adaptation method, based on the genetic optimization algorithm, that is incorporated into the recently proposed Gradient Descent Bit-Flipping Decoding with Momentum (GDBF-w/M). We show that the resulting decoder outperforms all state-of-the-art probabilistic bit-flipping decoders and, additionally, it can be trained to perform beyond BP decoding, which is verified by numerical examples that include codes used in IEEE 802.3an and 5GNR standards. The proposed framework provides a systematic method for decoder optimization without requiring knowledge of trapping sets. Moreover, it is applicable to both regular and irregular LDPC 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.