A unified approach to problems on guessing, source coding and encoding of tasks

Abstract

We study four problems namely, Campbell's source coding problem, Massey's guessing problem, Huieihel et al.'s memoryless guessing problem, and Bunte and Lapidoth's encoding of tasks problem. We observe a close relationship among these problems. In all these problems, the objective function to minimize is moments of some functions of random variables. R enyi entropy and the Sundaresan's divergence arise as optimal solutions. This motivates us to establish a connection between these four problems. In this thesis we nd a uni ed approach to solve all these problems. Indeed, we establish a general problem where all the problems are particular ones. We also compare our results with the existing ones. We strongly feel that this generalization would help us to understand the problems better and might help us apply in real life situations.