On the Capacity Achieving Probability Measures for Molecular Receivers

TL;DR

This paper analyzes the capacity of diffusion-based molecular communication systems with ligand receptor receivers, modeling the receiver as a finite-state Markov channel and identifying capacity-achieving probability measures.

Contribution

It introduces a capacity analysis framework for ligand receptor receivers modeled as finite-state Markov channels and characterizes capacity-achieving measures.

Findings

The i.i.d. capacity serves as a lower bound for the general capacity.

Finite support probability measures can achieve the i.i.d. capacity.

A bound on the number of points in the support of capacity-achieving measures is established.

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.