Zero-Error Capacity of the Chemical Residual Channel

We introduce a class of channels, collectively referred to as the ‘chemical residual channel’, where the channel output is a probabilistic function of the current input and the previous output. When the channel is binary, there are 81 possible cases. For all these cases with known or unknown initial state, we completely characterize the maximal rate that can be achieved with zero error probability at any given finite block length. As a result, the zero-error capacities of these cases are obtained. We also show that feedback does not increase the zero-error capacity.