Achievable rates for multiple descriptions

Author

Gamal, Abbas El ; Cover, Thomas M.

Volume

Issue

fYear

1982

fDate

11/1/1982 12:00:00 AM

Firstpage

851

Lastpage

857

Abstract

Consider a sequence of independent identically distributed (i.i.d.) random variables $X_{l},X_{2}, \\cdots , X_{n}$ and a distortion measure $d(X_{i},\\hat{X}_{i})$ on the estimates $\\hat{X}_{i}$ of $X_{i}$ . Two descriptions $i(X)\\in \\{1,2, \\cdots ,2^{nR_{1}} \\}$ and $j(X) \\in \\{1,2, \\cdots ,2^{nR_{2}} \\}$ are given of the sequence $X=(X_{1}, X_{2}, \\cdots ,X_{n})$ . From these two descriptions, three estimates $(i(X)), X2(j(X))$ , and $\\hat{X}_{O}(i(X),j(X))$ are formed, with resulting expected distortions $E frac{1/n} \\sum ^{n}_{k=1} d(X_{k}, \\hat{X}_{mk})=D_{m}, m=0,1,2.$ We find that the distortion constraints $D_{0}, D_{1}, D_{2}$ are achievable if there exists a probability mass distribution $p(x)p(\\hat{x}_{1},\\hat{x}_{2},\\hat{x}_{0}|x)$ with $Ed(X,\\hat{x}_{m})\\leq D_{m}$ such that $R_{1}> I(X;\\hat{X}_{1}),$ $R_{2}> I(X;\\hat{X}_{2}),$ where $I(\\cdot)$ denotes Shannon mutual information. These rates are shown to be optimal for deterministic distortion measures.

Keywords

Rate-distortion theory; Communication networks; Costs; Distortion measurement; Helium; Information theory; Mutual information; Random variables; Stochastic processes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1982.1056588

Filename

1056588

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=935652