On the Capacity Achieving Probability Measures for Molecular Receivers

Abstract: In this paper, diffusion-based molecular commu- nication with ligand receptor receivers is studied. Information messages are assumed to be encoded via variations of the con- centration of molecules. The randomness in the ligand reception process induces uncertainty in the communication; limiting the rate of information decoding. We model the ligand receptor receiver by a set of finite-state Markov channels and study the general capacity of such a receiver. Furthermore, the i.i.d. capacity of the receiver is characterized as a lower bound for the general capacity. It is also proved that a finite support probability measure can achieve the i.i.d. capacity of the receiver. Moreover, a bound on the number of points in the support of the probability measure is obtained.