On the reliability function for a noisy feedback Gaussian channel: Zero rate

A discrete-time channel with independent additive Gaussian noise is used for information transmission. There is also a feedback channel with independent additive Gaussian noise, and the transmitter observes all outputs of the forward channel without delay via this feedback channel. Transmission of a nonexponential number of messages is considered (i.e., the transmission rate is zero), and the achievable decoding error exponent for such a combination of channels is investigated. It is shown that for any finite noise in the feedback channel the achievable error exponent is better than the similar error exponent for a no-feedback channel. The transmission/decoding method developed in the paper strengthens the method earlier used by the authors for a BSC. In particular, for small feedback noise, it provides a gain of 23.6 % (instead of 14.3 % obtained earlier for a BSC).