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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 E^- (R) and an upper error exponent E^+ (R) . The lower error exponent E^- (R) exhibits an anomalous behavior in that E^- (R) increases monotonically from E^- (0) = 0 to E^- (C) = E(C) as the rate R increases from 0 to capacity.