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IEEE Communications Letters

Adaptive Gradient Descent Bit-Flipping Diversity Decoding

Srdan S. Brkic, Predrag Ivaniš, Bane V. Vasic

Published Jul 29, 2022• 10 citations
Publisher

Abstract

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.

DOI
10.1109/lcomm.2022.3195026

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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.
In this paper we propose a generalization of the recently published adaptive diversity gradient-descent bit flipping (AD-GDBF) decoder, named generalized AD-GDBF (gAD-GDBF) decoder. While the original AD-GDBF decoder was designed for the binary symmetric channel and used mostly to decode regular low-density parity-check codes, the gAD-GDBF algorithm incorporates several improvements which makes it eligible for the additive white Gaussian channel and decoding of arbitrary linear block code. The gAD-GDBF decoder uses the genetic algorithm to optimize a set of learnable parameters, for a targeted linear block code. The effectiveness of the proposed method is verified on short Bose-Chaudhuri-Hocquenghem (BCH) codes, where it was shown that for the same number of decoding iterations the gAD-GDBF decoder outperforms the belief-propagation decoder in terms of bit error rate and at the same time reduces the decoding complexity significantly.
In this paper, we introduce a novel gradient descent bit-flipping algorithm with a finite state machine (GDBF-wSM) for iterative decoding of low-density parity-check (LDPC) codes. The algorithm utilizes a finite state machine to update variable node potentials-for each variable node, the corresponding finite state machine adjusts the update value based on whether the node was a candidate for flipping in previous iterations. We also present a learnable framework that can optimize decoder parameters using a database of uncorrectable error patterns. The performance of the proposed algorithm is illustrated for various regular LDPC codes, both in a binary symmetric channel (BSC) and the channel with additive white Gaussian noise (AWGN). The numerical results indicate a performance improvement when comparing our algorithm to previously proposed GDBF-based approaches.
Bit-flipping (BF) is a very simple algorithm for decoding linear block codes. For the BF to achieve high performances of belief-propagation (BP) algorithms, which are far more complex, we apply several optimizations using the genetic algorithm (GA), to optimize the parameters of our decoder. Adaptive diversity gradient descent bit-flipping with momentum (AD-GDBFwM) algorithm is designed as a cascade of multiple decoders with different parameters, which are optimized with GA. In this paper we consider AD-GDBFwM decoding of mediumdensity parity-check (MDPC) codes. We measure the decoding performance and compare it with the results of various types of decoders, including BP and neural BP.
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.
It is known that the Gradient descent bit flipping (GDBF) algorithm is an effective hard-decision decoding algorithm for low-density parity-check (LDPC) codes. However, trapping in a local maximum limits its error-rate performance. This paper presents a modified GDBF scheme that can mitigate the trapping problem and hence can improve the error-rate performance. Compared to the conventional GDBF algorithm, the proposed method is able to improve the decoding performance of 0.3dB for an (18582, 16626) code. The (18582, 16626) LDPC decoder integrates 636k logic gates and achieves a throughput of 12.4 Gbps at a clock frequency of 200 MHz in a 90nm process.
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.