Adaptive Gradient Descent Bit-Flipping Diversity Decoding

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.

Automated summary

This paper proposes a novel framework for designing decoders for Low-Density Parity Check (LDPC) codes, which outperforms Belief-Propagation (BP) decoding on binary symmetric channels in terms of frame error rate performance. The framework incorporates an adaptation method based on the genetic optimization algorithm into the Gradient Descent Bit-Flipping Decoding with Momentum (GDBF-w/M). Numerical examples using codes from IEEE 802.3an and 5GNR standards verify the superior performance of the proposed decoder compared to state-of-the-art bit-flipping decoders. The framework provides a systematic method for decoder optimization without requiring knowledge of trapping sets, and is applicable to both regular and irregular LDPC codes.