We consider a Gaussian multiple-access channel with random user activity where the total
number of users ℓ n and the average number of active users kn may be unbounded. For this
channel, we characterize the maximum number of bits that can be transmitted reliably per
unit-energy in terms of ℓ n and k n. We show that if kn log ℓ n is sublinear in n, then each
user can achieve the single-user capacity per unit-energy. Conversely, if kn log ℓ n is
superlinear in n, then the capacity per unit-energy is zero. We further demonstrate that …

We consider a Gaussian multiple-access channel with random user activity where the total
number of userslₙ and the average number of active users kₙ may be unbounded. For this
channel, we characterize the maximum number of bits that can be transmitted reliably per
unit-energy in terms of lₙ and kₙ. We show that if kₙ log lₙ is sublinear in n, then each user
can achieve the single-user capacity per unit-energy. Conversely, if kₙ log lₙ is superlinear
in n, then the capacity per unit-energy is zero. We further demonstrate that orthogonal …