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Classical multiuser information theory studies the fundamental limits ofmodels with a fixed (often small) number of users as the coding blocklengthgoes to infinity. This work proposes a new paradigm, referred to as many-userinformation theory, where the number of users is allowed to grow with theblocklength. This paradigm is motivated by emerging systems with a massivenumber of users in an area, such as machine-to-machine communication systemsand sensor networks. The focus of the current paper is the many-access channelmodel, which consists of a single receiver and many transmitters, whose numberincreases unboundedly with the blocklength. Moreover, an unknown subset oftransmitters may transmit in a given block and need to be identified. A newnotion of capacity is introduced and characterized for the Gaussian many-accesschannel with random user activities. The capacity can be achieved by firstdetecting the set of active users and then decoding their messages.

Many-Access Channels: The Gaussian Case with Random User Activities