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In general, if there is one device A with the same performance as manydevices B, it would be better to replace many devices with one device. In orderto determine the number of devices that can be reduced, it is important todetermine the number of other devices B having the same performance as onedevice A. In this paper, based on the concept of "representing the performanceof one coding system A_n by the number of other coding systems B_n", weconsider the merits of an encoder that can access the side information in thefixed-length source coding in general sources. The purpose of this paper is tocharacterize the merit of being able to access the side information duringencoding with the number k_n of coding systems that can not access the sideinformation during encoding. For this purpose, we derive general formulas forthe upper limit of error probability and reliability functions without assuminga specific information theoretical structure. These general formulas areapplicable to various fields other than source coding problems, because theyhave been proved without assuming any particular information theoreticalstructure. We prove some theorems under the condition that the coding system issubadditive.

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