Gaussian many-access channels: Definition and symmetric capacity

This paper studies communication networks with a very large number of users simultaneously communicating with an access point. A new notion of many-access channel (MnAC) is introduced, which is the same as a multiaccess channel except that the number of users increases unboundedly with the coding block length. Unlike the conventional multiaccess channel with a fixed number of users, the joint typicality decoding technique is not directly applicable to establish the achievability of the capacity. It is shown that, as long as the number of users grows sublinearly with the coding block length, random coding with Feinstein's threshold decoding is sufficient to achieve the symmetric capacity of the Gaussian MnAC.