Performance bounds and optimal unear coding for multichannel communication systems

Abstract

ABSTRACT In this work design and evaluation of real-time implementable coding techniques for Gaussian multi-source multichannel communication systems are considered. In the discrete-time case n-dimensional Gaussian source outputs are to be transmitted over a memoryless noisy m-dimensional Gaussian channel under a given power constraint and a mean-squared-error distortion measure. The theoretical performance bounds (Shannon bounds) of this multi-source multichannel communication system are obtained through Optimum Performance Theoretically Attainable (OPTA) relationship between the source distortion and the channel power a. This relationship is obtained by equating R{$) = C(a)t that is the capacity-cost function C(a) of the vector channel and the rate-distortion function R($) of the vector source. Furthermore, it has been found that the optimum linear encoder results in a memoryless linear transformation while the decoder structure becomes a least-mean-square estimator. The performance of the linear encoder-decoder for the multi- source multichannel communication system is compared vis-a-vis OPTA bounds. It is shown that the performance of the optimal linear processors either coincides or is s/ery close to the Shannon bound in a number of significant cases. - n -- m - In the continuous-time case one considers a source emitting an n-dimensional Gaussian vector process to be transmitted for T seconds over an m-dimensional additive white Gaussian noise (WGN) channel. Further more, the transmission scheme involves a noiseless feedback channel. Under a quadratic distortion measure optimum linear encoder is found to be a time varying linear transformation while the decoder structure is a Kalman filter. It is shown that the optimal linear encoder-decoder pair attains the OPTA bounds when the channel is used on a time-sharing basis.