Abstract
In the information-spectrum methods proposed by Han and Verd´u, quantities defined using the ordinary limits superior/inferior in probability correspond to the optimal achievable rates in basic information-theoretic problems such as source coding and channel coding. In this paper, we introduce two more nonconventional limits in probability and apply all four limits to the fixed-length coding of a general source. In this paper, we first define four quantities for a source using the four limits in probability. It is shown that the four quantities satisfy a natural inequality if and only if the source is canonical. Next, we give operational meanings for the four quantities in fixed-length source coding. As one of the by-products, we can formulate nonconventional strong converse properties and obtain necessary and sufficient conditions. Finally, we explain a result for the achievable rate region in the optimistic sense of separately coding two correlated general sources. These results suggest the importance of the four quantities as new terminology for characterizing the performance of coding in more detail.
