Signaling with identical tokens: Lower bounds with energy constraints

As system sizes shrink to the nanoscale, the usual macroscopic methods of communication using electromagnetic and acoustic waves become increasingly difficult owing to, essentially, a mismatch between realizable antenna sizes and the propagation characteristics of the medium. Thus, at the scale of microns and below, communication methods which utilize molecular messengers become increasingly attractive, a notion supported by the ubiquity of molecular signaling in biological systems, usually with identical molecules. In a large portion of previous work, time-varying signal molecule/token concentration is used as the observable and various analyses performed. However, from an information-theoretic standpoint, concentration masks the underlying process which consists, fundamentally, of signal token emission, diffusion through some medium, and reception. In this paper we establish a lower bound on identical token signaling with energy constraints and thereby indirectly provide max-min bounds on concentration-based signaling rates.