Gaussian Broadcast Channels With Heterogeneous Finite Blocklength Constraints: Inner and Outer Bounds

We investigate the Gaussian broadcast channel with heterogeneous finite blocklength constraints (HB-GBC), which models different latency requirements for different users. To derive an outer bound on the rate region, we introduce a novel way of applying a Sato-type outer bound in the finite blocklength regime, since Sato’s classical outer bound is not directly applicable. To derive the achievable rate region, we present a way to use
shell codes
, which are second-order optimal for the single-user case, in the HB-GBC. We apply our technique to a hybrid TDMA/NOMA approach as well as
early decoding
, which is a technique that performs successive interference cancellation with an incompletely received interference codeword. Our numerical results show that the range of power allocations where early decoding is feasible is significantly enlarged compared to the state-of-the-art, leading to considerably improved rates in the regime where rate fairness between users is the goal. This makes early decoding a promising technique to increase the rates and fairness when strict latency constraints have to be met.