On weak convergence of probability measures, channel capacity and code error probabilities

Author

Schwarte, Heinrich

Author_Institution

Inst. for Exp. Math., Essen Univ., Germany

Volume

42

Issue

5

fYear

1996

fDate

9/1/1996 12:00:00 AM

Firstpage

1549

Lastpage

1551

Abstract

The relationship between weak convergence of channel probability measures, channel capacity, and error probability of block codes is examined for memoryless channels with general input and output alphabets. It is shown that channel capacity is a lower semi-continuous function and that every block code with maximal probability of error δ for a nominal channel for any ε>0 can be modified such that the modification has a probability of error less than δ+ε for all channels in a sufficiently small neighborhood of the nominal channel

Keywords

block codes; channel capacity; coding errors; convergence of numerical methods; error statistics; memoryless systems; probability; block codes; channel capacity; channel probability measures; code error probabilities; general input alphabet; general output alphabet; lower semicontinuous function; maximal error probability; memoryless channels; nominal channel; probability measures; weak convergence; Block codes; Capacity planning; Channel capacity; Convergence; Error probability; Gaussian channels; Information theory; Mathematics; Memoryless systems; Random variables;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.532897

Filename

532897