On the Zero-Error Capacity of the Chemical Residual Channel

We consider a class of channels, collectively referred to as the ‘chemical residual channel’, where the channel output is determined by the current input and the previous output. When the channel is binary and the output is a deterministic function of the current input and the previous output, there are 16 possible cases. For all these cases, we 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.