Capacity of Electron-Based Communication Over Bacterial Cables: The Full-CSI Case

Abstract

Motivated by recent discoveries of microbial communities that transfer electrons across centimeter-length scales, this paper studies the information capacity of bacterial cables via electron transfer, which coexists with molecular diffusion, under the assumption of full causal channel state information (CSI). The bacterial cable is modeled as an electron queue that transfers electrons from the encoder at the electron donor source, which controls the desired input electron intensity, to the decoder at the electron acceptor sink. Local clogging due to ATP saturation of the cells is modeled, as well as interference and leakage due to electron donors and acceptors along the cable. A discrete-time scheme is investigated, enabling the computation of an achievable rate. The regime of asymptotically small time-slot duration is analyzed, and the optimality of binary input distributions is proved, i.e., the encoder transmits at either maximum or minimum intensity, as dictated by the physical constraints of the cable. A dynamic programming formulation of the capacity is proposed, and the optimal binary signaling is determined via policy iteration. It is proved that the optimal signaling has smaller intensity than that given by the myopic policy , which greedily maximizes the instantaneous information rate but neglects its effect on the steady-state cable distribution. In contrast, the optimal scheme balances the tension between achieving high instantaneous information rate, and inducing a favorable steady-state distribution, such that those states characterized by high information rates are visited more frequently, thus revealing the importance of CSI. This work represents a first contribution towards the design of electron signaling schemes in complex microbial communities, e.g., bacterial cables and biofilms, where the tension between maximizing the transfer of information and guaranteeing the well-being of the overall bacterial community arises, and motivates further research on the design of more practical schemes, where CSI is only partially available.