  We study the problem of source and message compression in the one-shot
setting for the point-to-point and multi-party scenarios (with and without side
information). We derive achievability results for these tasks in a unified
manner, using the techniques of convex-split, which was introduced in
[Anshu,Devabathini and Jain 2014] and position-based decoding introduced in
[Anshu, Jain and Warsi 2017], which in turn uses hypothesis testing between
distributions. These results are in terms of smooth max divergence and smooth
hypothesis testing divergence. As a by-product of the tasks studied in this
work, we obtain several known source compression results (originally studied in
the asymptotic and i.i.d. setting) in the one-shot case.
  One of our achievability results includes the problem of message compression
with side information, originally studied in [Braverman and Rao 2011]. We show
that both our result and the result in [Braverman and Rao 2011] are near
optimal in the one-shot setting by proving a converse bound.
