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This paper establishes a close relationship among the four informationtheoretic problems, namely Campbell source coding, Arikan guessing, Huleihel etal. memoryless guessing and Bunte and Lapidoth tasks partitioning problems. Wefirst show that the aforementioned problems are mathematically related via ageneral moment minimization problem whose optimum solution is given in terms ofRenyi entropy. We then propose a general framework for the mismatched versionof these problems and establish all the asymptotic results using thisframework. Further, we study an ordered tasks partitioning problem that turnsout to be a generalisation of Arikan's guessing problem. Finally, with the helpof this general framework, we establish an equivalence among all theseproblems, in the sense that, knowing an asymptotically optimal solution in oneproblem helps us find the same in all other problems.

Are Guessing, Source Coding, and Tasks Partitioning Birds of a Feather?