Belief Propagation Decoding of Quantum LDPC Codes with Guided Decimation
Paper in proceeding, 2024

Quantum low-density parity-check (QLDPC) codes have emerged as a promising technique for quantum error correction. A variety of decoders have been proposed for QLDPC codes and many utilize belief propagation (BP) decoding in some fashion. However, the use of BP decoding for degenerate QLDPC codes is known to have issues with convergence. These issues are typically attributed to short cycles in the Tanner graph and error patterns with the same syndrome due to code degeneracy. In this work, we propose a decoder for QLDPC codes based on BP guided decimation (BPGD), which has been previously studied for constraint satisfaction and lossy compression problems. This decimation process is applicable to both binary and quaternary BP and it involves sequentially freezing the value of the most reliable qubits to encourage BP convergence. We find that BPGD significantly reduces the BP failure rate due to non-convergence, achieving performance on par with BP with ordered statistics decoding and BP with stabilizer inactivation, without the need to solve systems of linear equations. To explore how and why BPGD improves performance, we discuss several interpretations of BPGD and their connection to BP syndrome decoding.

Author

Hanwen Yao

Pratt School of Engineering

Duke University

Waleed Abu Laban

Student at Chalmers

Christian Häger

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

Alexandre Graell I Amat

Chalmers, Electrical Engineering, Communication, Antennas and Optical Networks

Henry D. Pfister

Duke University

Pratt School of Engineering

IEEE International Symposium on Information Theory - Proceedings

21578095 (ISSN)

2478-2483
9798350382846 (ISBN)

2024 IEEE International Symposium on Information Theory, ISIT 2024
Athens, Greece,

Subject Categories

Condensed Matter Physics

DOI

10.1109/ISIT57864.2024.10619083

More information

Latest update

9/17/2024