Layered Decoding of Quantum LDPC Codes

TL;DR

This paper introduces a layered decoding method for quantum LDPC codes that improves performance under hardware latency constraints, using novel scheduling techniques and code layer constructions.

Contribution

It presents a new layered decoding approach tailored for quantum LDPC codes, including a generic layer construction and a novel random order scheduling.

Findings

Random order scheduling reduces error floors in quantum LDPC decoding.

Layered decoding outperforms traditional flooded scheduling in quantum hardware settings.

The proposed methods improve decoding efficiency without additional post-processing.

Abstract

We address the problem of performing message-passing-based decoding of quantum LDPC codes under hardware latency limitations. We propose a novel way to do layered decoding that suits quantum constraints and outperforms flooded scheduling, the usual scheduling on parallel architectures. A generic construction is given to construct layers of hypergraph product codes. In the process, we introduce two new notions, t-covering layers which is a generalization of the usual layer decomposition, and a new scheduling called random order scheduling. Numerical simulations show that the random ordering is of independent interest as it helps relieve the high error floor typical of message-passing decoders on quantum codes for both layered and serial decoding without the need for post-processing.