Research on Hybrid Decoding of LDPC Codes Based on QUBO Modeling and Quantum Annealing

Abstract

Low-Density Parity-Check (LDPC) codes, as a class of high-efficiency error-correcting codes with sparse parity-check matrices, have demonstrated enormous potential in the field of communications since their rediscovery, and have become a core coding scheme especially in the fifth-generation (5G) wireless communication systems. To address the decoding problem of LDPC codes in complex channel environments, this paper proposes an innovative quantum-classical hybrid decoding architecture. By transforming the decoding problem into a Quadratic Unconstrained Binary Optimization (QUBO) problem, the architecture leverages the parallel processing capability of coherent optical quantum computers to accelerate the iterative decoding process. The research focuses on two typical scenarios specified in the 5G standard: the high-throughput scenario (dominated by BG1 with long code length and high code rate) and the low-complexity scenario (dominated by BG2 with short code length and low code rate). Through establishing a rigorous mathematical model, a hybrid decoder based on quantum annealing and the belief propagation algorithm is designed in this paper, and the Bayesian optimization method is adopted to adaptively adjust key parameters such as the maximum number of iterations and damping factor.  This research provides an important theoretical foundation and practical scheme for the practical application of quantum computing in the field of communications.