On Digital Communication Over a Discrete-Time Gaussian Channel with Noisy Feedback

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Abstract
We consider the problem of transmission of digital data over a discrete-time Gaussian channel with the use of a Gaussian feedback channel. We are particularly interested in the case where the signal-to-noise ratio in the feedback channel is finite. By making use of simple extension of P. Elias' scheme for transmitting analog data over this channel with feedback, we show that it is possible at some transmission rates to increase the error-exponent (reliability) compared to the error-exponent found by C. E. Shannon for the one-way channel. In particular at transmission rate zero, we show that the error-exponent can be improved by a factor of 1 + [ρ(1 + ρ)], where ρ and ρ are the forward and feedback signal-to-noise ratios respectively.

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