Source-channel diversity for parallel channels

We consider transmitting a source across a pair of independent, nonergodic channels with random states (e.g., slow-fading channels) so as to minimize the average distortion. The general problem is unsolved. Hence, we focus on comparing two commonly used source and channel encoding systems which correspond to exploiting diversity either at the physical layer through parallel channel coding or at the application layer through multiple description (MD) source coding. For on-off channel models, source coding diversity offers better performance. For channels with a continuous range of reception quality, we show the reverse is true. Specifically, we introduce a new figure of merit called the distortion exponent which measures how fast the average distortion decays with signal-to-noise ratio. For continuous-state models such as additive white Gaussian noise (AWGN) channels with multiplicative Rayleigh fading, optimal channel coding diversity at the physical layer is more efficient than source coding diversity at the application layer in that the former achieves a better distortion exponent. Finally, we consider a third decoding architecture: MD encoding with joint source-channel decoding. We show that this architecture achieves the same distortion exponent as systems with optimal channel coding diversity for continuous-state channels, and maintains the advantages of MD systems for on-off channels. Thus, the MD system with joint decoding achieves the best performance from among the three architectures considered, on both continuous-state and on-off channels.