Stabilizer Inactivation for Message-Passing Decoding of Quantum LDPC Codes

TL;DR

This paper introduces a stabilizer-inactivation method for message-passing decoding of quantum LDPC codes, improving convergence and reducing complexity compared to existing post-processing techniques.

Contribution

It presents a novel stabilizer-inactivation approach that enhances message-passing decoding performance and efficiency for quantum LDPC codes.

Findings

MP-SI outperforms MP-OSD in simulations

Reduced complexity compared to OSD-based methods

Effective across various quantum LDPC code constructions

Abstract

We propose a post-processing method for message-passing (MP) decoding of CSS quantum LDPC codes, called stabilizer-inactivation (SI). It relies on inactivating a set of qubits, supporting a check in the dual code, and then running the MP decoding again. This allows MP decoding to converge outside the inactivated set of qubits, while the error on these is determined by solving a small, constant size, linear system. Compared to the state of the art post-processing method based on ordered statistics decoding (OSD), we show through numerical simulations that MP-SI outperforms MP-OSD for different quantum LDPC code constructions, different MP decoding algorithms, and different MP scheduling strategies, while having a significantly reduced complexity.