Upper and Lower Bounds of Constrained Capacity in Diffusion-based Molecular Communication

Abstract

This paper investigates upper and lower bounds for the constrained capacity of a diffusive molecular communication (MC) system in the case where the information is associated with the concentration of molecules released by the transmitter. The evaluation of channel capacity for the diffusive channel is an open problem in the context of MC. Here, two simple bounds of the constrained capacity are derived for a given number of input concentration levels. Numerical results are reported for binary and quadruple concentration-shift keying considering the Poisson and Gaussian distributions, which are two common approximations used to describe the statistics of the received signal. We show that for both the two statistical channel models the resulting bounds are tight and, therefore, this means that, at least for low modulation orders, it is not necessary to resort to numerical techniques or complicated analytical expressions to guess the capacity of the diffusive MC channel.

Encoding, transmission, decoding, and specificity of calcium signals in plants

“…Recent progress in this area has led to mathematical models with the associated computational tools for answering such questions ( Farsad et al , 2016 ; Eckford and Thomas, 2018 ; Martins et al , 2019 ; Akyildiz et al , 2019 ; D. Bi et al , 2021 ). For instance, a framework for computing the channel capacity for a single ligand-activated channel has been derived ( Pagliara et al , 2014 ; Farsad et al , 2016 ; Thomas and Eckford, 2016 ; Ratti et al ., 2020 , 2021 ). It will be important to extend these results to multiple channels to evaluate the overall information transmission rates to gain insights into the encoding process.…”

Asymptotic MIMO Channel Model for Diffusive MC With Fully-Absorbing Receivers

“…Therefore, more recently, the evaluation of the capacity and bounds in diffusive MC channels with fully absorbing (FA) receivers was attempted. In [7], upper and lower bounds of the channel capacity were evaluated, assuming Poisson and Gaussian models for the statistical characterization of the received signal.…”