Abstract
This paper proposes a novelÌý technique Ìýto prove aÌý one - shot Ìýversion ofÌý achievability Ìý results ÌýinÌý network information Ìý theory . TheÌý technique Ìýis not based on covering and packing lemmas. In thisÌý 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. TheÌý technique Ìýis illustrated via four examples: point-to-point channel coding, Gelfand-Pinsker, broadcast channel and Berger-Tung problem of distributed lossy compression. Applying theÌý one - shot Ìý result Ìýfor 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, theseÌý results Ìýare employed in conjunction with multi-dimensional berry-esseen CLT toÌý derive new regions for finite-blocklength regime of Gelfand-Pinsker.