{
  "id": "cs/0701050",
  "version": "v2",
  "published": "2007-01-08T16:35:58.000Z",
  "updated": "2007-04-13T13:33:49.000Z",
  "title": "A Simple Proof of the Entropy-Power Inequality via Properties of Mutual Information",
  "authors": [
    "Olivier Rioul"
  ],
  "comment": "5 pages, accepted for presentation at the IEEE International Symposium on Information Theory 2007",
  "categories": [
    "cs.IT",
    "math.IT"
  ],
  "abstract": "While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the EPI hinge on integral representations of differential entropy using either Fisher's information (FI) or minimum mean-square error (MMSE). In this paper, we first present a unified view of proofs via FI and MMSE, showing that they are essentially dual versions of the same proof, and then fill the gap by providing a new, simple proof of the EPI, which is solely based on the properties of mutual information and sidesteps both FI or MMSE representations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-04-13T13:33:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mutual information",
      "simple proof",
      "entropy-power inequality",
      "properties",
      "shannons entropy power inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007cs........1050R"
    }
  }
}