Anytime communication over the Gilbert-Eliot channel with noiseless feedback

We study the reliability of sequential codes in a two-state Markov fading AWGN channel under the assumption of noiseless feedback and an average power constraint. We present a capacity achieving scheme with a doubly exponential anytime reliability function with respect to delay for every bit. The scheme is represented by a hybrid control system at the encoder in which the discrete system dynamics evolves based only on the channel state information while the continuous part of the state at the encoder reflects the evolution of the message uncertainty at the decoder. Whereas the classical Schalkwijk-Kailath scheme achieves double exponential reliability by exploiting the average nature of the power constraint to combat atypicality of the AWGN noise, our scheme also uses it to combat atypical fading realizations