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In a multi-access channel, completion time refers to the number of channel uses required for users, each with some given fixed bit pool, to complete the transmission of all their data bits. In this paper, the characterization of the completion time region is based on the concept of constrained rates, where users' rates are defined over possibly different number of channel uses. An information theoretic formulation of completion time is given and the completion time region is then established for two-user Gaussian multi-access channel, which, analogous to capacity region, characterizes all possible trade-offs between users' completion times.
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