One-shot source coding with coded side information available at the decoder

One-shot achievable rate region for source coding when coded side information is available at the decoder (source coding with a helper) is proposed. The achievable region proposed is in terms of conditional smooth max Rényi entropy and smooth max Rényi divergence. Asymptotically (in the limit of large block lengths) this region is quantified in terms of spectral-sup conditional entropy rate and spectral-sup mutual information rate. In particular, it coincides with the rate region derived in the limit of unlimited arbitrarily distributed copies of the sources.