Noisy feedback improves the Gaussian channel reliability function

For information transmission a discrete time channel with independent additive Gaussian noise is used. There is also a feedback channel with independent additive Gaussian noise, and the transmitter observes without delay all outputs of the forward channel via that noisy feedback channel. Transmission of nonexponential number of messages is considered and the achievable decoding error exponent for such a combination of channels is investigated. Transmission/decoding method used in the paper generalizes and strengthens the earlier method used by authors for BSC and Gaussian channel. It allows to improve essentially earlier results. In particular, for small feedback noise, it allows to gain 33.3% (instead of 23.6% in earlier papers).