  In the last few years, there has been a great interest in extending the
information-theoretic scenario for the non-asymptotic or one-shot case, i.e.,
where the channel is used only once. We provide the one-shot rate region for
the distributed source-coding (Slepian-Wolf) and the multiple-access channel.
Our results are based on defining a novel one-shot typical set based on smooth
entropies that yields the one-shot achievable rate regions while leveraging the
results from the asymptotic analysis. Our results are asymptotically optimal,
i.e., for the distributed source coding they yield the same rate region as the
Slepian-Wolf in the limit of unlimited independent and identically distributed
(i.i.d.) copies. Similarly for the multiple-access channel the asymptotic
analysis of our approach yields the rate region which is equal to the rate
region of the memoryless multiple-access channel in the limit of large number
of channel uses.
