On the Duality of Source and Channel Correlations: Slepian-Wolf Relaying Viewpoint

In this paper, we derive the theoretical outage probability of a transmission system in the presence of source and channel correlations in the block Rayleigh fading channels, based on the Slepian-Wolf theorem. Two transmitters and one common receiver are assumed, where the correlation knowledge between the two source information streams can be expressed as a bit-flipping model. The information bits at each transmitter are separately encoded and sent to a common decoder. In addition, we also assume the channels suffering from independent or correlated Rayleigh fading. It is known that the outage event happens when the instantaneous signal noise ratio (SNR) is lower than the given threshold ratio. This paper shows that the outage probability of the system model described above can be expressed by double integrals of the admissible rate region according to the Slepian-Wolf theorem, with respect to the joint probability density function (pdf) of the corresponding instantaneous signal amplitudes (or the equivalent SNRs) of the channels. The results show that the second order diversity of the theoretical outage curves can be achieved if and only if the two information streams are fully correlated, regardless of the channels being independent or not. On the contrary, the channel correlation makes opposite influence on the decay of the outage probability. However, if the two streams are not fully correlated, this influence gradually disappears as the average SNRs increases. In this sense, the source and channel correlation problems are dual with each other.