On the joint source-channel coding error exponent for systems with memory

We establish an upper bound for the joint source-channel coding (JSCC) error exponent E_J(Q, W) for a discrete stationary ergodic Markov (SEM) source Q and a discrete channel W with additive SEM noise. This bound, which is expressed in terms of the Renyi entropy rates of the source and noise processes, admits an identical form to Csiszar´s sphere-packing upper bound for the JSCC error exponent for memoryless systems (I. Csiszar, Nov. 1982). In this regard, our result is a natural extension of Csiszar´s upper bound of the JSCC error exponent from the case of memoryless systems to the case of SEM systems. We also investigate the analytical computation of E_J(Q,W) by comparing our bound with Gallager´s random-coding lower bound (R. G. Gallager, 1968), when the latter one is specialized to the SEM source-channel system