The landmark contribution by Schalkwijk and Kailath, on coding for additive channels by using feedback, offers a convenient coding scheme that has excellent properties in terms of the error exponent.
In this talk, we show that Schalkwijk and Kailath's scheme retains most of its desirable properties in the presence of uniformly quantized feedback. More specifically, for the additive white Gaussian channel with an input power constraint, we show that the achievable bit rate degrades continuously with the quantization error. In addition, we propose the first extension, of Schalkwijk and Kailath's scheme, for dealing with bounded noise in the feedback loop. We show that, even with an extra power constraint on the feedback loop, the achievable rate degrades continuously with the amplitude of the feedback noise.
This joint work with Tsachy Weissman.