Marsiglietti, Arnaud and Kostina, Victoria
(2017)
*A lower bound on the differential entropy for log-concave random variables with applications to rate-distortion theory.*
In:
2017 IEEE International Symposium on Information Theory (ISIT).
IEEE
, Piscataway, NJ, pp. 46-50.
ISBN 978-1-5090-4096-4.
http://resolver.caltech.edu/CaltechAUTHORS:20170816-162727008

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20170816-162727008

## Abstract

We derive a lower bound on the differential entropy for symmetric log-concave random variable X in terms of the p-th absolute moment of X, which shows that entropy and p-th absolute moment of a symmetric log-concave random variable are comparable. We apply our bound to study the rate distortion function under distortion measure |x − x|^r for sources that follow a log-concave probability distribution. In particular, we establish that the difference between the rate distortion function and the Shannon lower bound is at most log(√2e) ≈ 1.9 bits, independently of r and the target distortion d. For mean-square error distortion, the difference is at most log √πe ≈ 1.55 bits, regardless of d. Our results generalize to the case of vector X. Our proof technique leverages tools from convex geometry.

Item Type: | Book Section | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Related URLs: |
| |||||||||

ORCID: |
| |||||||||

Additional Information: | © 2017 IEEE. [AM] Supported by the Walter S. Baer and Jeri Weiss CMI Postdoctoral Fellowship. [VK] Supported in part by the National Science Foundation (NSF) under Grant CCF-1566567. | |||||||||

Funders: |
| |||||||||

Subject Keywords: | Differential entropy, rate-distortion function, Shannon lower bound, log-concave distribution | |||||||||

Record Number: | CaltechAUTHORS:20170816-162727008 | |||||||||

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20170816-162727008 | |||||||||

Official Citation: | A. Marsiglietti and V. Kostina, "A lower bound on the differential entropy for log-concave random variables with applications to rate-distortion theory," 2017 IEEE International Symposium on Information Theory (ISIT), Aachen, Germany, 2017, pp. 46-50. doi: 10.1109/ISIT.2017.8006487 | |||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||

ID Code: | 80529 | |||||||||

Collection: | CaltechAUTHORS | |||||||||

Deposited By: | Kristin Buxton | |||||||||

Deposited On: | 16 Aug 2017 23:32 | |||||||||

Last Modified: | 16 Aug 2017 23:32 |

Repository Staff Only: item control page