This paper considers a Gaussian multiple-access channel with random user activity where
the total number of users and the average number of active users may grow with the
blocklength. For this channel, it studies the maximum number of bits that can be transmitted
reliably per unit-energy as a function of and. When all users are active with probability one,
ie,, it is demonstrated that, if is of an order strictly below, then each user can achieve the
single-user capacity per unit-energy (where is the noise power) by using an orthogonal …

This paper considers a Gaussian multiple-access channel with random user activity where
the total number of users ℓn and the average number of active users kn may grow with the
blocklength n. For this channel, it studies the maximum number of bits that can be
transmitted reliably per unit-energy as a function of ℓn and kn. When all users are active with
probability one, ie, ℓn= kn, it is demonstrated that, if kn is of an order strictly below n/logn,
then each user can achieve the single-user capacity per unit-energy (loge)/N0 (where N0/2 …