{
  "id": "2102.07122",
  "version": "v1",
  "published": "2021-02-14T10:29:58.000Z",
  "updated": "2021-02-14T10:29:58.000Z",
  "title": "Refined Belief-Propagation Decoding of Quantum Codes with Scalar Messages",
  "authors": [
    "Kao-Yueh Kuo",
    "Ching-Yi Lai"
  ],
  "comment": "to be published in Proc. IEEE Global Commun. Conf. (GLOBECOM), 2020",
  "categories": [
    "quant-ph",
    "cs.IT",
    "math.IT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-14T10:29:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum codes",
      "scalar messages",
      "refined belief-propagation decoding",
      "binary stabilizer codes needs",
      "performance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}