Simultaneous Information and Energy Transmission: A Finite Block-Length Analysis

In this paper, a non-asymptotic analysis of the fundamental limits of simultaneous information and energy transmission (SIET) is presented. The notion of the information-energy capacity region, i.e., the largest set of simultaneously achievable information and energy rates, is revisited in a context in which transmissions occur within a finite number of channel uses and strictly positive decoding error probability (DEP) and energy shortage probability (ESP) are tolerated. The focus is on the case of one transmitter, one information receiver and one energy harvester communicating through binary symmetric memoryless channels. In this case, some outer bounds on the information transmission rate and the energy transmission rate are presented. More specifically, given a finite block-length, a DEP, and an ESP, four scenarios arise depending on whether an average or maximal probability constraint is imposed on the DEP and the ESP. For each scenario, the limits on the information rate and energy rate beyond which a transmission is no longer possible are presented (impossibility results). These results reveal the competitive interaction between the information transmission and energy transmission tasks identifying a certain regime in which increasing the information rate necessarily implies decreasing the energy rate and vice versa.