Asymptotic properties of delay-time-weighted probability of error (Corresp.)

Author

Krich, Steven I.

Volume

Issue

fYear

1974

fDate

3/1/1974 12:00:00 AM

Firstpage

278

Lastpage

279

Abstract

Asymptotic properties of expected distortion are studied for the delay-time-weighted probability of error distortion measure $d_n(x,\\tilde{x}) = n^{-1} \\sum _{t=0}^{n-1} f(t + n)[l - \\delta (x_t,\\tilde{x}_t)]$ ,, where $x = (x_0,x_1,\\cdots ,x_{n-1})$ and $\\tilde{x} = (\\tilde{x}_0,\\tilde{x}_1,\\cdots ,\\tilde{x}_{n-1})$ are source and reproducing vectors, respectively, and $\\delta (\\cdot, \\cdot)$ is the Kronecker delta. With reasonable block coding and transmission constraints $x_t$ is reproduced as $\\tilde{x}_t$ with a delay of $t + n$ time units. It is shown that if the channel capacity is greater than the source entropy $C > H(X)$ , then there exists a sequence of block length $n$ codes such that $E[d_n(X,\\tilde{X})] rigjhtarrow 0$ as $n \\rightarrow \\infty$ even if $f(t) \\rightarrow \\infty$ at an exponential rate. However, if $f(t)$ grows at too fast an exponential rate, then $E[d_n(X,\\tilde{X})] \\rightarrow \\infty$ as $n \\rightarrow \\infty$ . Also, if $C < H(X)$ and $f(t) \\rightarrow \\infty$ then $E[d_n(X,\\tilde{X})] \\rightarrow \\infty$ as $n \\rightarrow \\infty$ no matter how slowly $f(t)$ grows.

Keywords

Rate-distortion theory; Source coding; Block codes; Channel capacity; Decoding; Delay effects; Distortion measurement; Entropy; Length measurement; Stochastic processes; Time measurement; Weight control;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1974.1055183

Filename

1055183

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=921296