Convergence to the rate-distortion function for Gaussian sources

Author

Bunin, Barry J. ; Wolf, Jack K.

Volume

17

Issue

1

fYear

1971

fDate

1/1/1971 12:00:00 AM

Firstpage

65

Lastpage

70

Abstract

In this paper we derive an expression for the minimum-mean-square error achievable in encoding $t$ samples of a stationary correlated Gaussian source. It is assumed that the source output is not known exactly but is corrupted by correlated Gaussian noise. The expression is obtained in terms of the covariance matrices of the source and noise sequences. It is shown that as $t \\rightarrow \\infty$ , the result agrees with a known asymptotic result, which is expressed in terms of the power spectra of the source and noise. The rate of convergence to the asymptotic results as a function of coding delay is investigated for the case where the source is first-order Markov and the noise is uncorrelated. With $D$ the asymptotic minimum-mean-square error and $D_t$ the minimum-mean-square error achievable in transmitting $t$ samples, we find $\\mid D_t - D \\mid \\leq O((t^{-1} \\log t) ^ {1/2})$ when we transmit the noisy source vectors over a noiseless channel and $\\mid D_t - D \\mid \\leq O((t^{-1} \\log t)^ {1/3})$ when the channel is noisy.

Keywords

Gaussian processes; Rate-distortion theory; Source coding; Convergence; Covariance matrix; Delay; Filters; Gaussian noise; Laboratories; Random variables; Rate-distortion; Telephony; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1971.1054576

Filename

1054576