On the error probability for a class of binary recursive feedback strategies

The error probability for a class of binary recursive feedback strategies is evaluated. An exact analysis is given for both a nonsequential and a sequential decision strategy. We obtain the interesting result that even for the nonsequential receiver the error probability vanishes exponentially fast at channel capacity. A similar result had been previously obtained by Horstein for the sequential receiver, but was believed to be a consequence of the sequential nature of his decision strategy. For rates below capacity our feedback strategies have two error exponents, i.e., a lower error exponent and an upper error exponent . The lower error exponent exhibits an anomalous behavior in that increases monotonically from to as the rate increases from 0 to capacity.