Reverse hypercontractivity region for the binary erasure channel

In this paper, we obtain the reverse hypercontractive region for the pair of variables (X, Y) where X is a uniformly distributed binary random variable and Y (a ternary random variable) is obtained by passing X through a symmetric binary erasure channel (BEC), for a non-trivial range of parameters. The technique used builds on two recent results: a) characterization of reverse hypercontractivity using information measures, and b) computation of the forward hypercontractive region for the BEC.