The Zero Error Capacity of a Noisy Channel

The zero error capacity C 0 of a noisy channel is defined to be the least upper bound of rates at which it is possible to transmit information with zero probability of error. Various properties of C 0 are studied; upper and lower bounds and methods of evaluation of C 0 are given. Inequalities are obtained for the C 0 relating to the ?>sum?> and ?>product?> of two given channels. The analogous problem of zero error capacity C 0F for a channel with a feedback link is considered. It is shown that while the ordinary capacity of a memoryless channel with feedback is equal to that of the same channel without feedback, the zero error capacity may be greater. A solution is given to the problem of evaluating C 0F.