Achieving Optimal Distortion Exponent of Parallel Quasi-Static Fading Channel with Imperfect CST

We consider transmission of a continuous amplitude i.i.d. source over a M parallel quasi-static Rayleigh fading channels. Due to the non-ergodic nature of the channel, Shannon´s source-channel separation theorem does not hold and the optimal performance requires a joint optimization of the source and channel variables. Our goal in this paper is to characterize the expected end-to-end source distortion in the high SNR regime. Defining source distortion exponent as Delta = - lim_SNRrarrinfin log ED/ SNR, we derive the optimal distortion exponent for any bandwidth expansion ratio b. Our optimality is with respect to system with perfect channel state information at the transmitter (CSIT) and thus refers to the best achievable performance. In particular, we prove the achievability of the source distortion exponent upper bound, derived by considering ergodic channel, with both rate adaptive channel coding diversity and source coding diversity scheme where only imperfect CSIT is available. Although we consider a memoryless Gaussian source in this paper, the derived optimal distortion exponent holds for a general class of source distribution.