Suppose X is a uniformly distributed n-dimensional binary vector and Y is obtained by passing X through a binary symmetric channel with crossover probability α. A recent conjecture by Courtade and Kumar postulates that I(F(X); Y ) ≤ 1 - h(α) for any Boolean function F. So far, the best known upper bound was essentially I(F(X); Y ) ≤ (1 - 2α)2. In this paper, we derive a new upper bound that holds for all balanced functions, and improves upon the best known previous bound for α > 1 over 3.
|Original language||American English|
|Title of host publication||Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||5|
|State||Published - 10 Aug 2016|
|Event||2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain|
Duration: 10 Jul 2016 → 15 Jul 2016
|Name||IEEE International Symposium on Information Theory - Proceedings|
|Conference||2016 IEEE International Symposium on Information Theory, ISIT 2016|
|Period||10/07/16 → 15/07/16|
Bibliographical noteFunding Information:
The work of O. Ordentlich was supported by the MIT - Technion postdoctoral fellowship. The work of O. Shayevitz was supported by an ERC grant no. 639573, a CIG grant no. 631983, and an ISF grant no. 1367/14. The work of O. Weinstein was supported by a Simons Society Junior Fellowship
© 2016 IEEE.