Information Transmission Over Fading Channels

We consider the lossy transmission of source information over Rayleigh fading channels. We investigate the utility of two channel capacity definitions, ergodic capacity, where it is assumed that the channel cycles through all 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 lossy transmission of source information over wireless networks. We 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. We also introduce different performance measures that take into account the variance of source distortion and might be more suitable for source transmission over fading channels. Finally, we observe that in a Rayleigh fading channel in the presence of channel state information (CSI) at both the transmitter and receiver, 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 average source distortion increases with an increase in average signal to noise ratio (SNR) while the probability of achieving the average capacity does not change significantly with SNR.