Multistage Universal Coding in Discrete Channels with Feedback

A multistage stochastic encoding and decoding procedure in systems with feedback is given; it is suitable for arbitrary discrete ergodic channels. The decoding algorithm is maximally simple, since it employs only error detection at a given stage. It is shown that, in any discrete ergodic channel with noiseless feedback, this procedure (without adaptation to the channel state) ensures that the error probability decreases exponentially for a constant mean transmission rate.