The capacity-cost function of discrete additive noise channels with and without feedback

We consider modulo-q additive noise channels, where the noise process is a stationary irreducible and aperiodic Markov chain of order le, We begin by investigating the capacity-cost function (C(beta)) of such additive-noise c hannels without feedback, We establish a tight upper bound to (C(beta)) whi ch holds for general (not necessarily Markovian) stationary q-ary noise pro cesses. This bound constitutes the counterpart of the Wyner-Ziv lower bound to the rate-distortion function of stationary sources with memory, We also provide two simple lower bounds to C(beta) which along with the upper boun d can be easily calculated using the Blahut algorithm for the computation o f channel capacity. Numerical results indicate that these bounds form a tig ht envelope on C(beta). We nest examine the effect of output feedback on the capacity-cost function of these channels and establish a lower bound to the capacity-cost functio n with feedback (C-FB(beta)). We show (both analytically and numerically) t hat for a particular feedback encoding strategy and a class of Markov noise sources, the lower bound to C-FB(beta) is strictly greater than C(beta). T his demonstrates that feedback can increase the capacity-cost function of d iscrete channels with memory.