Linear feedback rate bounds for regressive channels (Corresp.)

Author

Butman, S.

Volume

Issue

fYear

1976

fDate

5/1/1976 12:00:00 AM

Firstpage

363

Lastpage

366

Abstract

This article presents new tighter upper bounds on the rate of Gaussian autoregressive channels with linear feedback. The separation between the upper and lower bounds is small. We have $frac{1}{2} \\ln \\left( 1 + \\rho \\left( 1+ \\sum _{k=1}^{m} \\alpha _{k} x^{- k} \\right)^{2} \\right) \\leq C_{L} \\leq frac{1}{2} \\ln \\left( 1+ \\rho \\left( 1+ \\sum _{k = 1}^{m} \\alpha _{k} / \\sqrt {1 + \\rho} \\right)^{2} \\right), mbox{a\\ll \\rho}$ , where $\\rho = P/N_{0}W, \\alpha _{l}, \\cdots , \\alpha _{m}$ are regression coefficients, $P$ is power, $W$ is bandwidth, $N_{0}$ is the one-sided innovation spectrum, and $x$ is a root of the polynomial $(X^{2} - 1)x^{2m} - \\rho \\left( x^{m} + \\sum ^{m}_{k=1} \\alpha _{k} x^{m - k} \\right)^{2} = 0.$ It is conjectured that the lower bound is the feedback capacity.

Keywords

Autoregressive processes; Feedback communication; Bandwidth; Channel capacity; Colored noise; Feedback; Forward contracts; Information theory; Mathematics; Propulsion; Space technology; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1976.1055548

Filename

1055548

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=925084