Relations between universal FV and FF source codes

Universal lossless source coding for general sources are considered. Our results reveal that the definition of the universality of fixed-to-variable length coding (FV coding) based on the redundancy criterion is not equivalent to the one based on the average codeword length criterion. Moreover, it is clarified that, when we adopt the redundancy criterion, the existence of a universal FV code implies the existence of a universal fixed-to-fixed length code (FF code). On the other hand, it is also clarified that, when we adopt the average codeword length criterion, the existence of a universal FV code does not imply the existence of a universal FF code. Further, the relation between universal source coding and universal hypothesis testing is also investigated.