Non-asymptotic covering lemmas

In information theory, the packing and covering lemmas are conventionally used in conjunction with the typical sequence approach in order to prove the asymptotic achievability results for discrete memoryless systems. In contrast, the single-shot approach in information theory provides non-asymptotic achievability and converse results, which are useful to gauge the backoff from the asymptotic fundamental limits due to fixed blocklength, and which do not rely on discrete/memoryless assumptions. This paper reviews the non-asymptotic covering lemmas we have obtained recently and their application in single-user and multiuser information theory.