Recurrent Multiple-Repetition Coding for Channels With Feedback

We consider multiple repetition strategies with fixed delay decoding for discrete memoryless channels with noiseless feedback. Existing binary schemes by Schalkwijk and Zigangirov are analyzed and their results are extended. The general error exponents are computed and presented by elegant expressions in the strictly symmetric case. An important class of precoded sequences, so-called flip sequences, is found and their degrading effect on the error exponent is investigated. This effect is shown negligible when the repetition parameters are chosen such that the transmission rate is maximized. Even when signalling at channel capacity, the error exponent is shown to be strictly positive.