An asymptotic expression for the information and capacity of a multidimensional channel with weak input signals

Author

Prelov, Vyacheslav V. ; Van der Meulen, Edward C.

Author_Institution

Inst. for Problems of Inf. Transmission, Acad. of Sci., Moscow, Russia

Volume

39

Issue

5

fYear

1993

fDate

9/1/1993 12:00:00 AM

Firstpage

1728

Lastpage

1735

Abstract

An asymptotic expression is derived for the Shannon mutual information between the input and output signals for a relatively large class of continuous alphabet memoryless channels in the case of weak input signals, when the input space is multidimensional. The authors extend a result of Ibragimov and Khas´minskii (1972) from the one-dimensional to the N-dimensional case. The asymptotic expression obtained relates the Shannon (1948) mutual information function and the Fisher information matrix. This expression is used to derive an asymptotic expression for the capacity of continuous alphabet memoryless channels with vector-valued weak input signals. This asymptotic capacity involves the largest eigenvalue of the Fisher information matrix evaluated at the zero input signal

Keywords

channel capacity; eigenvalues and eigenfunctions; information theory; matrix algebra; Fisher information matrix; Shannon mutual information function; asymptotic capacity; asymptotic expression; channel capacity; continuous alphabet memoryless channels; eigenvalue; multidimensional channel; multidimensional input space; vector-valued signals; weak input signals; zero input signal; Artificial intelligence; Capacity planning; Channel capacity; Convolution; Entropy; Gaussian noise; Information theory; Memoryless systems; Multidimensional systems; Mutual information;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.259667

Filename

259667