مرکز منطقه ای اطلاع رساني علوم و فناوري - Achievable rates for multiple descriptions

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.