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"THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD" In this paper, we employ a broadcast transmission strategy for studying multiple access communication with no channel state information (CSI) at the transmitter. Users simultaneously encode their data into several streams that are then superimposed on top of each other. The receiver decodes a subset of the transmitted streams, dependent on the quality of the channel. We focus on two particular problems: first, we analyze communication over a Gaussian multiple access channel (MAC) with slow fading and no transmitter CSI. Users encode one stream per each fading state. We characterize the fundamental tradeoff between the achievable sum-rates in the various data streams. Next, we study transmission over a two- user synchronous Gaussian MAC in which users transmit in an uncoordinated and random manner. Each user superimposes two data streams, one high priority, ensuring part of the information is received reliably, and one high rate, opportunistically taking advantage of the channel when the other user is not transmitting. We study the performance limit for low and high SNR regimes.