Non-asymptotic and second-order achievability bounds for source coding with side-information

We present a novel achievability bound for the Wyner-Ahlswede-Körner (WAK) problem of lossless source coding with rate-limited side-information. This bound is proved using ideas from channel simulation and channel resolvability. The bound improves on all previous non-asymptotic bounds on the error probability of the WAK problem. We also present achievable second-order coding rates by applying the multidimensional Berry-Essèen theorem to our new non-asymptotic bound.