  Future wireless access networks aim to simultaneously support a large number
of devices with heterogeneous service requirements, including data rates, error
rates, and latencies. While achievable rate and capacity results exist for
Gaussian broadcast channels in the asymptotic blocklength regime, the
characterization of second-order achievable rate regions for heterogeneous
blocklength constraints is not available. Therefore, we investigate a two-user
Gaussian broadcast channel (GBC) with heterogeneous blocklength constraints,
specified according to users' channel output signal-to-noise ratios (SNRs). We
assume the user with higher output SNR has a shorter blocklength constraint. We
show that with sufficiently large output SNR, the stronger user can perform the
\textit{early decoding} (ED) technique to decode and subtract the interference
via successive interference cancellation (SIC). To achieve it, we derive an
explicit lower bound on the necessary number of received symbols for a
successful ED, using an independent and identically distributed Gaussian input.
A second-order rate of the weaker user who suffers from an SNR change due to
the heterogeneous blocklength constraint, is also derived. Numerical results
show that ED can outperform the hybrid non-orthogonal multiple access scheme
when the stronger channel is sufficiently better than the weaker one. Under the
considered setting, about 7-dB SNR gain can be achieved. These results shows
that ED with SIC is a promising technique for the future wireless networks.
