One-Shot Mutual Covering Lemma and Marton's Inner Bound with a Common Message

TL;DR

This paper introduces a one-shot mutual covering lemma to establish a new achievability bound for broadcast channels with a common message, connecting it to Marton's inner bound and channel resolvability.

Contribution

It develops a one-shot mutual covering lemma and derives a new achievability bound that generalizes Marton's inner bound with a deterministic encoder.

Findings

Achieves a one-shot bound for broadcast with a common message

Recovers Marton's inner bound in the i.i.d. case

Links mutual covering lemma to channel resolvability

Abstract

By developing one-shot mutual covering lemmas, we derive a one-shot achievability bound for broadcast with a common message which recovers Marton's inner bound (with three auxiliary random variables) in the i.i.d.~case. The encoder employed is deterministic. Relationship between the mutual covering lemma and a new type of channel resolvability problem is discussed.