A new class of channel models with memory is presented in order to study various kinds of interference phenomena. It is shown, among other things, that when all other parameters are held fixed, channel capacity

is an {em increasing} function of the memory length, while the cutoff rate

generally is a {em decreasing} function. Calculations with various explicit coding schemes indicate that

is better than

as a performance measure for these channel models. As a partial resolution of this

versus

paradox, the conjecture is offered that

is more properly a measure of coding delay rather than of coding complexity.