One-shot mutual covering lemma and Marton´s inner bound with a common message

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.