On coding for source with infinitesimal time slots

We introduce a source that emits symbols at infinitesimal time slots. The source may emit no symbol at a slot. The outputs from the source are encoded on the real-time basis. We derive the minimum loss probability and reveal a connection to the continuous model. Moreover, we define the utilization factor of the channel and show that it coincides with the loss probability for any code. We consider the situation in which the number of division of time unit goes infinity keeping the entropy rate constant. In this artificial case, the process does not approach to a Poisson process. We show that the ordinary entropy coding is not optimal but sub-optimal.