Refined Belief-Propagation Decoding of Quantum Codes with Scalar Messages

Kao Yueh Kuo, Ching Yi Lai

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

Codes based on sparse matrices have good performance and can be efficiently decoded by belief-propagation (BP). Decoding binary stabilizer codes needs a quaternary BP for (additive) codes over GF(4), which has a higher check-node complexity compared to a binary BP for codes over GF(2). Moreover, BP decoding of stabilizer codes suffers a performance loss from the short cycles in the underlying Tanner graph. In this paper, we propose a refined BP algorithm for decoding quantum codes by passing scalar messages. For a given error syndrome, this algorithm decodes to the same output as the conventional quaternary BP but with a check-node complexity the same as binary BP. As every message is a scalar, the message normalization can be naturally applied to improve the performance. Another observation is that the message-update schedule affects the BP decoding performance against short cycles. We show that running BP with message normalization according to a serial schedule (or other schedules) may significantly improve the decoding performance and error-floor in computer simulation.

Original languageEnglish
Title of host publication2020 IEEE Globecom Workshops, GC Wkshps 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728173078
DOIs
StatePublished - Dec 2020
Event2020 IEEE Globecom Workshops, GC Wkshps 2020 - Virtual, Taipei, Taiwan
Duration: 7 Dec 202011 Dec 2020

Publication series

Name2020 IEEE Globecom Workshops, GC Wkshps 2020 - Proceedings

Conference

Conference2020 IEEE Globecom Workshops, GC Wkshps 2020
CountryTaiwan
CityVirtual, Taipei
Period7/12/2011/12/20

Keywords

  • belief-propagation
  • LDPC codes
  • message normalization
  • message-update schedule
  • Quantum stabilizer codes
  • sparse matrices
  • sum-product algorithm

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