Optimal linear coding for vector channels

The problem of optimal coding (minimum-least-squared-error linear transformation) of vector signals is considered. The source is a time-discrete memoryless Gaussian vector source and the channel is k-dimensional with channel noise being a k-dimensional white Gaussian stationary vector sequence. The optimal encoder is a linear transformation process that matches the r-dimensional signal vector and the k-dimensional channel under the given channel power constraint. The eigenvalues of the signal covariance matrix and the noise covariance matrix together with a performance weighting matrix determine the optimum coder design. An inverse eigenvalue problem must be solved if the individual subchannel powers are constrained.