On the feedback capacity of a discrete non-binary noise channel with memory

We study the feedback capacity of a discrete binary-input non-binary output channel with memory recently introduced in [5] to model soft-decision demodulated time-correlated fading channels. The channel, whose output process can be explicitly expressed in terms of its binary input process and a non-binary noise process, encompasses modulo-additive noise binary channels as a special case (realized when hard-decision demodulation is used on the underlying fading channel). We show that, even though the channel has memory, feedback does not increase its capacity when the noise process is stationary ergodic. We also note the validity of the result for arbitrary noise processes.