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The diversity gain function is a unified metric for the asymptotic error performance of wireless communication systems. In this correspondence, we propose a theorem that relates the diversity gain function and the coding gain to the probability density function of the instantaneous signal-to-noise ratio (SNR) at the origin. It provides a general framework for analyzing the asymptotic reliability of wireless communication systems in the presence of fading. As two applications of the proposed theorem, we evaluate two relay selection schemes in fixed-gain amplify-and-forward (AF) cooperative networks. The results show that even if not all channel state information is available at the destination, fixed-gain AF relay selection schemes can still achieve full cooperative diversity and near optimal error performance. This is an outstanding merit that instantaneous-gain AF relay selection schemes do not possess [Y. Jing and H. Jafarkhani, “Single and multiple relay selection schemes and their achievable diversity orders,” IEEE Trans. WIRELESS COMMUN., vol. 8, no. 3, pp. 1414-1423, Mar. 2009].