Capacity of a Randomized Channel with Feedback and Matching of the Source

An expression is obtained for the capacity of a Gaussian randomized channel with feedback with limiting of the mean input signal power in time and given spectral density of the additive noise and fading probability density. It is proved that by linear encoding and decoding of the signal combined with permutation of the spectral components of the message together with permutation of its time segments along such a channel, it is possible to transmit messages forming a Gaussian random process so that the resulting mean square error is minimal.