A Method of Expressing the Magnitude of Merit of Being Able to Access a Side Information During Encoding

In general, if there is one device A with the same performance as many devices B, it would be better to replace many devices with one device. In order to determine the number of devices that can be reduced, it is important to determine the number of other devices B having the same performance as one device A. In this paper, based on the concept of "representing the performance of one coding system A_n by the number of other coding systems B_n", we consider the merits of an encoder that can access the side information in the fixed-length source coding in general sources. The purpose of this paper is to characterize the merit of being able to access the side information during encoding with the number k_n of coding systems that can not access the side information during encoding. For this purpose, we derive general formulas for the upper limit of error probability and reliability functions without assuming a specific information theoretical structure. These general formulas are applicable to various fields other than source coding problems, because they have been proved without assuming any particular information theoretical structure. We prove some theorems under the condition that the coding system is subadditive.Comment: 29 pages, 4 figure