A technique for deriving one-shot achievability results in network information theory
Proceedings of the IEEE International Symposium on Information Theory, Istanbul, Turkey, July 2013
Abstract

This paper proposes a novel  technique  to prove a  one - shot  version of  achievability   results  in  network information   theory . The  technique  is not based on covering and packing lemmas. In this  technique , we use a stochastic encoder and decoder with a particular structure for coding that resembles both the ML and the joint-typicality coders. Although stochastic encoders and decoders do not usually enhance the capacity region, their use simplifies the analysis. The Jensen inequality lies at the heart of error analysis, which enables us to deal with the expectation of many terms coming from stochastic encoders and decoders at once. The  technique  is illustrated via four examples: point-to-point channel coding, Gelfand-Pinsker, broadcast channel and Berger-Tung problem of distributed lossy compression. Applying the  one - shot   result  for the memoryless broadcast channel in the asymptotic case, we get the entire region of Marton's inner bound without any need for time-sharing. Also, these  results  are employed in conjunction with multi-dimensional berry-esseen CLT to  derive new regions for finite-blocklength regime of Gelfand-Pinsker.