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In this paper, we develop theory for speaker recognition, based on information theory. We show that the performance of a speaker recognition system is closely connected to the mutual information between features and speaker, and derive upper and lower bounds for the performance. We apply the theory to the case when the speech is coded and transmitted over a packet-based channel, in which packet losses occurs. The theory gives important insights in what methods can be used to improve the recognition performance, and what methods are meaningless.