  We present novel non-asymptotic or finite blocklength achievability bounds
for three side-information problems in network information theory. These
include (i) the Wyner-Ahlswede-Korner (WAK) problem of almost-lossless source
coding with rate-limited side-information, (ii) the Wyner-Ziv (WZ) problem of
lossy source coding with side-information at the decoder and (iii) the
Gel'fand-Pinsker (GP) problem of channel coding with noncausal state
information available at the encoder. The bounds are proved using ideas from
channel simulation and channel resolvability. Our bounds for all three problems
improve on all previous non-asymptotic bounds on the error probability of the
WAK, WZ and GP problems--in particular those derived by Verdu. Using our novel
non-asymptotic bounds, we recover the general formulas for the optimal rates of
these side-information problems. Finally, we also present achievable
second-order coding rates by applying the multidimensional Berry-Esseen theorem
to our new non-asymptotic bounds. Numerical results show that the second-order
coding rates obtained using our non-asymptotic achievability bounds are
superior to those obtained using existing finite blocklength bounds.
