A General Coding Scheme for Signaling Gaussian Processes Over Gaussian Decision Models

In this paper, we transform the n-finite transmission feedback information (FTFI) capacity of unstable Gaussian decision models with memory on past outputs, subject to an average cost constraint of quadratic form derived in [1], into controllers-encoders-decoders that control the output process, encode a Gaussian process, reconstruct the Gaussian process via a mean-square error (MSE) decoder, and achieve the n-FTFI capacity. For a Gaussian RV message X N(0,σ²X) it is shown that the MSE decays according to E X-X'n n²= -2C0, n(k)σX², Kɞ(kmin,∞), where C0, n(k) is the n-FTFI capacity, and kmin is the threshold on the power to ensure convergence.