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International Conference on Electrical, Electronic and Computing Engineering (IcETRAN)

Gradient Descent Decoding of MDPC Codes Optimized with Genetic Algorithm

Dimitrije Jovanović, Jovan Milojković, Zoran Čiča, Predrag Ivaniš

Published Jun 9, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1109/icetran66854.2025.11114132

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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.
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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 analyze the performances of iterative decoders for linear block codes. In particular, we consider two modifications of the gradient-descent bit flipping (GDBF) algorithm with momentum, where multiple component decoders with different momentum values are concatenated to improve the decoder performance. The learning parameters of the component decoders are obtained by using a Genetic algorithm based on the database of the uncorrectable error patterns of the previous decoder. We present three optimization strategies and provide a comparison with the state-of-the-art decoders. The numerical results are presented on short Bose-Chaudhuri-Hocquenghem (BCH) codes and the channel with additive white Gaussian noise (AWGN).
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.