  A standard assumption in the design of ultra-reliable low-latency
communication systems is that the duration between message arrivals is larger
than the number of channel uses before the decoding deadline. Nevertheless,
this assumption fails when messages arrive rapidly and reliability constraints
require that the number of channel uses exceed the time between arrivals. In
this paper, we consider a broadcast setting in which a transmitter wishes to
send two different messages to two receivers over Gaussian channels. Messages
have different arrival times and decoding deadlines such that their
transmission windows overlap. For this setting, we propose a coding scheme that
exploits Marton's coding strategy. We derive rigorous bounds on the achievable
rate regions. Those bounds can be easily employed in point-to-point settings
with one or multiple parallel channels. In the point-to-point setting with one
or multiple parallel channels, the proposed achievability scheme outperforms
the Normal Approximation, especially when the number of channel uses is smaller
than $200$. In the broadcast setting, our scheme agrees with Marton's strategy
for sufficiently large numbers of channel uses and shows significant
performance improvements over standard approaches based on time sharing for
transmission of short packets.
