Joint Source–Channel Coding Error Exponent for Discrete Communication Systems With Markovian Memory

We study the error exponent, E_J, for reliably transmitting a discrete stationary ergodic Markov (SEM) source Q over a discrete channel W with additive SEM noise via a joint source-channel (JSC) code. We first establish an upper bound for E_J in terms of the Renyi entropy rates of the source and noise processes. We next investigate the analytical computation of E_J by comparing our bound with Gallager´s lower bound (1968) when the latter one is specialized to the SEM source-channel system. We also note that both bounds can be represented in Csiszar´s form (1980), as the minimum of the sum of the source and channel error exponents. Our results provide us with the tools to systematically compare E_J with the tandem (separate) coding exponent E_J. We show that as in the case of memoryless source-channel pairs E_J les 2E_r and we provide explicit conditions for which E_J > E_T. Numerical results indicate that E_J ap 2E_T for many SEM source-channel pairs, hence illustrating a substantial advantage of JSC coding over tandem coding for systems with Markovian memory.