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In this paper, we consider a Rayleigh fading half-duplex system where multiple source-destination pairs communicate with the help of a single relay. The relay performs the analog network coding (ANC) to assist the transmissions from the sources to the destinations, which is a well-known amplify-and-forward-based protocol. We derive the closed-form expressions for outage probabilities in the high-SNR regime for the system with an arbitrary number of the source-destination pairs. The diversity-multiplexing tradeoff (DMT) of the ANC is also derived, which is based on the outage probabilities. It is shown that the derived outage probabilities match the results of Monte Carlo simulations in the high-SNR regime. The ANC is shown to achieve the same DMT as the xor network coding strategy that assumes an ideal condition that each destination node perfectly overhears the data from other sources.