Quantum Approximate Optimization for Decoding of Low-Density Parity-Check Codes

TL;DR

This paper introduces a quantum algorithm-based decoding method for LDPC codes that outperforms traditional belief propagation in accuracy, leveraging quantum optimization to improve decoding reliability in noisy environments.

Contribution

It presents a novel QAOA-based decoding framework for LDPC codes, integrating quantum optimization with classical decoding constraints for improved performance.

Findings

QAOA-based decoder outperforms BP in decoding accuracy

Higher probability of correct codeword recovery with QAOA

Effective in high-noise and short-length code scenarios

Abstract

Decoding Low-Density Parity-Check (LDPC) codes is a fundamental problem in coding theory, and Belief Propagation (BP) is one of the most popular methods for LDPC code decoding. However, BP may encounter convergence issues and suboptimal performance, especially for short-length codes and in high-noise channels. The Quantum Approximate Optimization Algorithm (QAOA) is a type of Variational Quantum Algorithm (VQA) designed to solve combinatorial optimization problems by minimizing a problem-specific cost function. In this paper, we present a QAOA-based decoding framework for LDPC codes by formulating a decoding cost function that incorporates both parity-check constraints and soft channel reliability information. The resulting optimization problem is solved using QAOA to search for low-energy configurations corresponding to valid codewords. We test the proposed method through extensive numerical experiments and compare its performance with BP decoding. The experimental results demonstrate that the QAOA-based decoder achieves a higher probability of correctly recovering the transmitted codeword than BP across multiple experimental settings.