Diversity in Diffusion-Based Molecular Communication Channel with Drift Derya Malak Hamideh Ramezani Murat Kocaoglu Ozgur B. Akan Next-generation and Wireless Communications Laboratory Department of Electrical and Electronics Engineering Koc University, Istanbul, Turkey Email:{dmalak,hramezani13,mkocaoglu,akan}@ku.edu.tr Abstract—We utilize the well known Additive Inverse Gaussian Noise (AIGN) communication channel to investigate the effect of diversity in diffusion-based molecular communication with drift, where the transmitter releases different types of molecules to the fluid medium by encoding the information onto the release time and type of molecules. The fluid channel imposes extra delay on the communication, and the receiver decodes the encoded information by solely utilizing the molecular arrival times. In this paper, simple receiver models based on maximum likelihood estimation (MLE) are investigated. Furthermore, upper and lower bounds on the capacity of AIGN communication channel with molecular diversity are derived. Index Terms—Molecular communication, Diffusion, Drift, AIGN channel, Channel capacity, Receiver model, Maximum likelihood estimation I. I NTRODUCTION AIGN channel model is widely used in modeling the delay caused by the drift of the fluid media in molecular commu- nication [1]–[4]. In this paper, we focus on the information encoding on the transmission time and type of the molecules by using the AIGN channel with molecular diversity. In our model, the transmitter is capable of releasing a diver- sity of molecules according to a predefined delay distribution. We also assume that there is an abundance of molecules inside the transmitter. The channel is a fluid channel with a positive drift for all the molecule types. Hence, the channel delay can be modeled by the AIGN distribution [2]. Simple receivers, which are capable of storing the timing information of the molecules are presented. The receivers are unable to recognize the molecules identities directly. Instead, they categorize the received molecules based on their arrival times. For future practical applications of molecular communi- cation [5], [6], transmitting information through the timing and type of the released molecules will be a more realistic model compared to the one in which the information is solely encoded in the molecules’ release time. On the other hand, the ability of detecting the molecule type directly complicates the receiver. Thus, we focus on simple receivers which can decode transmitted message and detect the molecule types based on the molecules’ arrival time statistics. We also provide the upper and lower capacity bounds for the AIGN communication channel with molecular diversity. Our objective is to point out the rate improvement by using a variety of molecules, compared to the AIGN channel with a single molecule type. The remainder of this paper is organized as follows. In Section II, we give a model for the AIGN communication channel with molecular diversity. In Section III, we provide simple receiver models to decode the transmitted message by the AIGN channel with low design complexity. In Section IV, to characterize the achievable performance of the AIGN communication channel, we provide the upper and lower bounds on the capacity of the molecular channel based on the receiver characteristics. Then, in Section V, we compare the derived capacity bounds for AIGN channel with molecular diversity. We also evaluate the performance of the proposed receivers in detecting type of molecule and estimating the information encoded in the release time of molecules. Finally, we conclude the paper in Section VI. II. AIGN CHANNEL WITH MOLECULAR DIVERSITY A molecular communication system based on the release and transmission of the signaling molecules of the same type is analyzed in [2]. Furthermore, an information theoretical model for the additive inverse Gaussian noise (AIGN) channel is derived in the same work. Here, we aim to extend this model to a multi-molecular type communication system. Hence, we consider the AIGN channel with molecular diversity. We aim to observe how the diversity of the transmitted molecules affects the communication performance in fluid medium. A. Transmitter Model The transmitter first determines the molecule type to be released. The molecule type is denoted by a random variable T . We assume that there are M types of molecules with each having the release probability of Pr(T = i)= α i , i ∈{1,...,M }, (1) where α i denotes the release probability of molecule type i. The information that the transmitter wants to communicate with the selected molecule type is denoted by random variable X. We assume the general case that distribution of X depends on type of the selected molecule. The transmitter encodes this information in the release time of molecules, denoted by random variable R. After determining the molecule type and release time, a set of m molecules is released to the fluid medium based on the following scenarios: