We study the best exponential decay in the blocklength of the probability of error that can be achieved in the transmission of a single bit over the Gaussian channel with an active noisy Gaussian feedback link. We impose an expected block power constraint on the forward link and study both almost-sure and expected block power constraints on the feedback link. In both cases the best achievable error exponents are finite and grow approximately proportionally to the larger between the signal-to-noise ratios on the forward and feedback links. The error exponents under almost-sure block power constraints are typically strictly smaller than under expected constraints. Some of the results extend to communication at arbitrary rates below capacity and to general discrete memoryless channels.
In REF , which is closer to our interactive setting, the reliability function associated with the transmission of a single bit over an AWGN channel with noisy active feedback has been considered.
Error Exponents for the Gaussian Channel With Active Noisy Feedback
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science Mathematics