Unequal Message Protection: One-Shot analysis via Poisson Matching Lemma

The Poisson Matching Lemma (PML) introduced by Li & Anantharam (IT-Trans 2021) is a powerful technique for one-shot analysis of a variety of multi-terminal source and channel coding problems. In this work we make use of PML to derive one-shot achievability results for unequal message protection with a fixed number of message classes. Our analysis involves revisiting the proof of the PML to account for the error associated with each codebook at the decoder. Our approach leads to compact bounds on the error probability for each message class for arbitrary input distributions and channels. For the example of binary erasure channel, we compare our bounds numerically with prior work [1] and demonstrate improvements in the achievable rate.