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arXiv:2411.16203

Iterative Gradient Descent Decoding for Real Number LDPC Codes

Oana Boncalo, Alexandru Amaricăi

Published Nov 25, 2024• 0 citations
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Abstract

This paper proposes a new iterative gradient descent decoding method for real number parity codes. The proposed decoder, named Gradient Descent Symbol Update (GDSU), is used for a class of low-density parity-check (LDPC) real-number codes that can be defined with parity check matrices which are similar to those of the binary LDPC from communication standards such as WiFi (IEEE 802.11), 5G. These codes have a simple and efficient two stage encoding that is especially appealing for the real number field. The Gradient optimization based decoding has been a relatively simple and fast decoding technique for codes over finite fields. We show that the GDSU decoder outperforms the gradient descent bit-flipping (GDBF) decoder for rates $1/2$, $2/3$, and has similar decoding performance for the $3/4$ rate of the IEEE 802.11 codes standard.

DOI
10.48550/arxiv.2411.16203

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This paper proposes a new iterative gradient descent decoding method for real number parity codes. The proposed decoder, named Gradient Descent Symbol Update (GDSU), is used for a class of low-density parity-check (LDPC) real-number codes that can be defined with parity check matrices which are similar to those of the binary LDPC from communication standards such as WiFi (IEEE 802.11), 5G. These codes have a simple and efficient two stage encoding that is especially appealing for the real number field. The Gradient optimization based decoding has been a relatively simple and fast decoding technique for codes over finite fields. We show that the GDSU decoder outperforms the gradient descent bit-flipping (GDBF) decoder for rates 1/21/21/2, 2/32/32/3, and has similar decoding performance for the 3/43/43/4 rate of the IEEE 802.11 codes standard.
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.
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.
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.
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.