On the Capacity of Point-to-Point and Multiple-Access Molecular Communications With Ligand-Receptors

Abstract

In this paper, we consider the bacterial point-to-point and multiple-access molecular communications with ligand-receptors. For the point-to-point communication, we investigate common signaling methods, namely the Level Scenario (LS), which uses one type of a molecule with different concentration levels, and the Type Scenario (TS), which employs multiple types of molecules with a single concentration level. We investigate the trade-offs between the two scenarios from the capacity point of view. We derive an upper bound on the capacity using a Binomial Channel (BIC) model and the symmetrized Kullback-Leibler (KL) divergence. A lower bound is also derived when the environment noise is negligible. For the TS, we also consider the effect of blocking of a receptor by a different molecule type. Then, we consider multipleaccess communications, for which we investigate three scenarios based on molecule and receptor types, i.e., same types of molecules with Different Labeling and Same types of Receptors (DLSR), Different types of Molecules and Receptors (DMDR), and Same types of Molecules and Receptors (SMSR). We investigate the trade-offs among the three scenarios from the total capacity point of view. We derive some inner bounds on the capacity region of these scenarios when the environment noise is negligible. * This paper has been presented in part at the IEEE International Symposium on Information Theory (ISIT), Wan Chai, Hong Kong, June 2015.DRAFT arXiv:1509.05877v1 [cs.IT] 19 Sep 2015 examine the instantaneous effect of the multiple-access interference instead of its average value. In the following, we first concentrate on a point-to-point molecular communication and evaluate its capacity and the upper and lower bounds. Then we consider three multiple-access scenarios and for each, we evaluate the capacity region and some inner bounds.Our main contributions are as follows:• Point-to-Point Communication: We investigate the trade-offs between two bacterial point-to-point communication scenarios for ligand-receptors with fixed total number of molecules and receptors: (a) multi-type molecular communication with a single concentration level, and (b) single-type molecular communication with multiple concentration levels. At the first glance, scenario (a) introduces new degrees of freedom and reduces the intersymbol interference (ISI). However, since the number of molecules per type (the power per type) reduces increasing the number of types, we should examine the benefit of using different types of molecules. To make the comparison between scenario (a) and (b), we adopt the model of [8] in this work. In addition, a Markov model for the interactions between different types of molecules near the receptor is presented and the capacity for this model is computed numerically.• Upper and Lower Bounds for the BIC Capacity: Using KL divergence bound of [14], we derive an upper bound on the capacity of the point-to-point BIC model under given average and peak constraints on the channel input (Theorem 1). Based on numerical eviden...

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