On the asymptotic error probability of composite relay channels

Consider the composite relay channel consisting of a set of relay channels associated to a probability measure. The current channel is a draw from its probability and in some cases arbitrary small error probability cannot be guaranteed for all channels in the set. In this paper, instead of finding the maximum achievable rate subject to a small error probability (EP) for all the channels in the set, we look at the asymptotic behavior of EP for a given rate. The notion of achievable EP is introduced as a novel performance measure for wireless relay channels. We can intuitively define it as the smallest EP that can be asymptotically achieved for a given rate. The behavior of EP is directly related to the ∈-capacity of each channel in the set. It is shown that the behavior of EP is upper and lower bounded by the outage probability of a region which is referred to as the full error region. Then every code with a rate belonging to this region yields EP equal to one. Finally, new coding for oblivious cooperation simultaneously exploiting both Decode-and-Forward (DF) and Compress-and-Forward (CF) strategies is investigated. The Gaussian relay channel with slow fading is also discussed.