Solutions to a class of minimax decision problems arising in communication systems
Abstract
Consideration is given to a class of minimax decision problems arising in the transmission of a Gaussian vector message over a vector channel which is conditionally Gaussian and is subjected to jamming noise with unknown probabilistic description other than the power constraint. The derivation of the best linear encoder and decoder structures which would minimize a quadratic distortion measure at the output of the receiver under worst choices for jamming noise statistics is discussed. A saddlepoint solution is found to exist when the linear encoder structure is of the mixed type but does not exist when it is restricted to be deterministic. The saddlepoint solution depends on two integervalued parameters: one determines the number of components of the message vector to be transmitted through the channel and the other determines the number of channels that the jammer actually jams.
 Publication:

Journal of Optimization Theory Applications
 Pub Date:
 December 1986
 Bibcode:
 1986JOTA...51..375B
 Keywords:

 Jamming;
 Minimax Technique;
 Random Noise;
 Statistical Decision Theory;
 Telecommunication;
 Channels (Data Transmission);
 Saddle Points;
 Signal To Noise Ratios;
 Communications and Radar