Decoding Quantum LDPC Codes using Collaborative Check Node Removal

TL;DR

This paper introduces a collaborative decoding framework for quantum LDPC codes that enhances the min-sum algorithm's success rate by selectively removing stabilizer check nodes based on information measurements.

Contribution

It presents a novel collaborative decoding strategy combining message passing with check node removal, improving decoding performance for quantum LDPC codes.

Findings

Improved decoding success rates on GHP codes

Mitigation of trapping sets without significant overhead

Introduction of 'qubit separation' concept and information measurements

Abstract

Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and efficient decoders. Iterative message passing-based decoders, although fast, fail to produce suitable success rates due to the colossal degeneracy and short cycles intrinsic to these codes. In this work we present a strategy to improve the performance of the Belief Propagation (BP) decoding, specifically the min-sum algorithm. We propose a collaborative decoding framework that integrates message passing with stabilizer check node removals. We further introduce the concept of ``qubit separation" and show that the improved decoding performance is directly related to the generation of highly separated trapped data qubits. To guide a more selective removal of check nodes that constrain the separation of the trapped data qubits, we introduce information measurements (IMs) for the data qubits and their adjacent stabilizer checks. We evaluate the performance of the proposed collaborative decoder on Generalized Hypergraph Product (GHP) codes and demonstrate that appropriate decoder configurations mitigate trapping sets in min-sum decoding without significant overhead.