On the Zero-Error Capacity of the Modulo-Additive Noise Channel With Help

The zero-error helper capacity of the modulo-additive noise channel is studied both in the presence and in the absence of feedback. In its presence, a complete solution of said capacity is provided. In its absence, a solution is provided when the alphabet size is prime. For all other cases, upper and lower bounds are derived, and a necessary and sufficient condition for positivity is provided. Thanks to the help, the zero-error capacity may increase by more than the help's rate, and it can be positive yet smaller than one bit.