Gaussian red alert exponents: Geometry and code constructions

In non-block “streaming” data settings it has been observed that the availability of feedback dramatically changes the attainable communication reliability as a function of delay. The codebooks upon which these results depend contain a special and extremely reliable “red alert” message, used to indicate to the decoder when its best guess of the prior transmission is erroneous. In this paper we develop analogous results for additive white Gaussian channels that operate under both average and peak power constraints. We derive achievable error exponents for the special message for all rates up to capacity and provide geometric intuition for our coding scheme and error analysis.