Rateless codes for the Gaussian multiple access channel

We consider communication over the Gaussian multiple access channel (MAC) with unknown set of active users. The proposed multiple access strategy is distributed and achieves a maximum sum rate point on the boundary of the capacity region for this channel for any set of active users S simultaneously, as if S were known at the transmitters. The proposed coding scheme splits each user into a set of virtual users, each of which can be decoded using a single-user decoder at the receiver instead of having to decode all users jointly. We also present a generalization of this scheme to the case where the channel gains differ between users and each user only knows its own channel gain.