
For FullText PDF, please login, if you are a member of IEICE,
or go to Pay Per View on menu list, if you are a nonmember of IEICE.

NonAsymptotic Bounds and a General Formula for the RateDistortion Region of the Successive Refinement Problem
Tetsunao MATSUTA Tomohiko UYEMATSU
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E101A
No.12
pp.21102124 Publication Date: 2018/12/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E101.A.2110
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications) Category: Shannon theory Keyword: general source, information spectrum, nonasymptotic bound, ratedistortion region, successive refinement,
Full Text: PDF(804.7KB) >>Buy this Article
Summary:
In the successive refinement problem, a fixedlength sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by one of two codewords, and the other reconstruction is obtained by all two codewords. For this coding problem, we give nonasymptotic inner and outer bounds on pairs of numbers of codewords of two encoders such that each probability that a distortion exceeds a given distortion level is less than a given probability level. We also give a general formula for the ratedistortion region for general sources, where the ratedistortion region is the set of rate pairs of two encoders such that each maximum value of possible distortions is less than a given distortion level.

