Iterative Gradient Descent Decoding for Real Number LDPC Codes

TL;DR

This paper introduces GDSU, a novel iterative gradient descent decoding method for real number LDPC codes, demonstrating improved performance over existing gradient-based decoders for certain code rates.

Contribution

The paper presents a new gradient descent-based decoding algorithm, GDSU, tailored for real number LDPC codes with standard-like parity check matrices, enhancing decoding efficiency and performance.

Findings

GDSU outperforms GDBF for rates 1/2 and 2/3.

GDSU achieves similar performance to GDBF at 3/4 rate.

The method is simple, fast, and suitable for codes used in WiFi and 5G standards.

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.