Superposition coding (SC) has been known to be capacity-achieving for the Gaussian memoryless broadcast channel for more than 30 years. However, SC regained interest in the context of non-orthogonal multiple access (NOMA) in 5G. From an information theory point of view, SC is capacity-achieving in the broadcast Gaussian channel, even when the number of users tends to infinity. However, using SC has two drawbacks: the decoder complexity increases drastically with the number of simultaneous receivers, and the latency is unbounded since SC is optimal only in the asymptotic regime. To evaluate these effects quantitatively in terms of fundamental limits, we introduce a finite time transmission constraint imposed at the base station, and we evaluate fundamental trade-offs between the maximal number of superposed users, the coding block-length and the block error probability. The energy efficiency loss due to these constraints is evaluated analytically and by simulation. Orthogonal sharing appears to outperform SC for hard delay constraints (equivalent to short block-length) and in low spectral efficiency regime (below one bit per channel use). These results are obtained by the association of stochastic geometry and finite block-length information theory.
Keywords: finite block-length; information theory; many-user Gaussian broadcast channel; massive access; non-orthogonal multiple access; superposition coding.