{
  "id": "1707.04413",
  "version": "v1",
  "published": "2017-07-14T08:37:50.000Z",
  "updated": "2017-07-14T08:37:50.000Z",
  "title": "The Mutual information of LDGM codes",
  "authors": [
    "Jan van den Brand",
    "Nor Jaafari"
  ],
  "categories": [
    "cs.IT",
    "math.IT",
    "math.PR"
  ],
  "abstract": "We provide matching upper and lower bounds on the mutual information in noisy reconstruction of parity check codes and thereby prove a long-standing conjecture by Montanari [IEEE Transactions on Information Theory 2005]. Besides extending a prior concentration result of Abbe and Montanari [Theory of Computing 2015] to the case of odd check degrees, we precisely determine the conjectured formula for code ensembles of arbitrary degree distribution, thus capturing a broad class of capacity approaching codes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-14T08:37:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94A17",
      "68Q87"
    ],
    "keywords": [
      "mutual information",
      "ldgm codes",
      "prior concentration result",
      "odd check degrees",
      "arbitrary degree distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}