The zero error capacity of a noisy channel

The zero error capacity
C_o
of a noisy channel is defined as the least upper bound of rates at which it is possible to transmit information with zero probability of error. Various properties of
C_o
are studied; upper and lower bounds and methods of evaluation of
C_o
are given. Inequalities are obtained for the
C_o
relating to the "sum" and "product" of two given channels. The analogous problem of zero error capacity
C_oF
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_oF
.