Ergodic capacity, outage capacity, and information transmission over Rayleigh fading channels

We consider the lossy transmission of source information over Rayleigh fading channels. We investigate the usefulness of various channel capacity definitions, namely ergodic capacity, where it is assumed that the channel transitions over all the fading states, and outage capacity, where the source is transmitted at a constant rate with a specified outage probability. We also study the outage rate and expected source distortion for different outage probabilities. It is observed that the outage probabilities required to maximize outage rate and minimize expected distortion are quite different. This implies that schemes based on maximizing capacity might not lead to the most efficient design for the lossy transmission of source information over wireless networks. We also show that minimizing expected distortion over a wireless link does not necessarily minimize the variance of the distortion, and hence parameter selection based on minimizing expected distortion can lead to a high distortion for a specific realization. Finally, we observe that in a Rayleigh fading channel, in addition to a capacity distribution, there is a source distortion distribution at the receiver for a memoryless Gaussian source. A careful investigation of the capacity and source distortion distributions reveal that the probability of achieving the expected source distortion increases with an increase in average signal to noise ratio (SNR) unlike the case of ergodic capacity.