Capacity of electron-based communication over bacterial cables: The full-CSI case with binary inputs

Motivated by recent discoveries of multi-cellular microbial communities that transfer electrons across centimeter-length scales, this paper studies the information capacity of bacterial cables via electron transfer, which may coexist with the more well-known communication strategies based on molecular diffusion. The bacterial cable is modeled as an electron queue, which transports electrons from the encoder to the decoder located at the two ends of the cable. The encoder controls the desired input electron intensity, whereas the decoder attempts to decode the transmitted message based on the measured output electron process. Clogging of the cable, induced by local ATP saturation and resulting in a loss of electron transport efficiency along the cable, is modeled. The case where both the encoder and the decoder have full causal channel state information (CSI) with binary inputs is studied. A discrete-time version of the system is considered, enabling the computation of an achievable rate for the continuous-time system, based on known results on the capacity of finite-state Markov channels. The regime of asymptotically small time-slot duration is studied, and it is shown that the capacity optimization problem can be recast as a Markov decision process, which enables the use of standard optimization algorithms, e.g., policy iteration, to compute the capacity and the optimal expected desired input electron intensity, which generates the binary signal.