Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices

TL;DR

This paper introduces a neural belief propagation decoding method for quantum LDPC codes using overcomplete check matrices, significantly improving decoding performance and reducing latency in quantum error correction.

Contribution

It proposes a novel decoding approach utilizing redundant check matrices and neural networks, enhancing performance over traditional belief propagation methods for quantum LDPC codes.

Findings

Enhanced decoding accuracy with overcomplete check matrices

Reduced decoding latency in quantum error correction

Further performance gains with neural belief propagation

Abstract

The recent success in constructing asymptotically good quantum low-density parity-check (QLDPC) codes makes this family of codes a promising candidate for error-correcting schemes in quantum computing. However, conventional belief propagation (BP) decoding of QLDPC codes does not yield satisfying performance due to the presence of unavoidable short cycles in their Tanner graph and the special degeneracy phenomenon. In this work, we propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix. This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency. Furthermore, we propose a novel neural belief propagation decoder based on the quaternary BP decoder of QLDPC codes which leads to further decoding performance improvements.