On Using Noisy Feedback in a Gaussian Channel

For information transmission, a discrete-time channel with independent additive Gaussian noise is used. There is also another channel with independent additive Gaussian noise (the feedback channel), and the transmitter observes all outputs of the forward channel without delay via that channel. Transmission of nonexponentially many messages is considered (i.e., the transmission rate is zero), and the achievable decoding error exponent for such a combination of channels is investigated. The transmission method strengthens the method previously used by the authors for the BSC and Gaussian channels. In particular, for small feedback noise, this yields a gain of 33.3% (instead of 23.6% earlier in the similar case of a Gaussian channel).