Capacity Bounds for Diffusive Molecular Communication over Discrete-time Compound Poisson Channels

Diffusive molecular communication (DMC) is a paradigm which promises realizing nanonetworks for healthcare applications. DMC systems in in vivo environments may face biological entities which may act as external noise sources. Recently, the diffusion channel in the presence of the biological entities releasing molecules of the same type with information molecules has been particularly modeled as a Poisson channel whose background noise rate is stochastic. In this letter, the capacity and performance of the communication over this newly introduced channel model is investigated. Upper bounds on the capacity are proposed based on the cascade representations of this channel. Correspondingly, lower bounds on the error probability of communication over this channel are derived. Our results reveal that each bound may be preferred depending on the system parameters.