Bound on the average transmission time for sequential estimation systems containing an additive Gaussian noise channel

Author

Kadota, T.T. ; Wyner, Aaron D. ; Ziv, Jacob

Volume

Issue

fYear

1971

fDate

9/1/1971 12:00:00 AM

Firstpage

514

Lastpage

515

Abstract

We consider the class of sequential estimation systems containing additive Gaussian noise channels. Let $m$ be a random variable representing the source and $x(t),y(t)$ be stochastic processes representing the signal and the channel output, respectively. Denote by $\\hat{m}$ an estimate of $m$ based on observing $y(t)$ from 0 to $\\tau$ , where $\\tau$ is a random variable determined by a certain stopping rule of the decoder depending on a realization of $y$ . Let $d(m,\\hat{m})$ be the distortion of $\\hat{m}$ relative to $m$ and $R(\\cdot)$ be the rate distortion function of $m$ with respect to the distortion measure $d$ . Denote by $P_o$ and $N_o$ the available average signal power and the noise power level, respectively. We show that $E_{\\tau } \\geq (2 N_o / P_o)R. (Ed(m,\\hat{m}))$ and hence $Ed(m,\\hat{m}) \\geq R ^ {-1} (P_o E_ \\tau /2N_o )$ .. That is, given the average distortion $Ed(m,\\hat{m})$ , the average transmission time required can be no smaller than $(2N_o/P_o)R(Ed(m,\\hat{m}))$ . Conversely, given the average transmission time $E_{\\tau }$ , the average distortion can be no smaller than $R ^ {-1} (P_o E _ {\\tau } /2N_o)$ .

Keywords

Gaussian processes; Sequential estimation; Additive noise; Decoding; Distortion measurement; Gaussian noise; Mutual information; Random variables; Rate-distortion; Signal processing; Stochastic processes; Telephony;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1971.1054693

Filename

1054693

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=916273