Capacity Bounds for Diffusive Molecular Communication Over Discrete-Time Compound Poisson Channels
Abstract: Diffusive molecular communication (DMC) is a paradigm which promises realizing nano networks for healthcare applications. DMC systems in in vivo environments may face biological entities which may act as external noise sources. Recently, the diffusion channel in the presence of the biological entities releasing molecules of the same type with information molecules has been particularly modeled as a Poisson channel whose background noise rate is stochastic. In this letter, the capacity and performance of the communication over this newly introduced channel model is investigated. Upper bounds on the capacity are proposed based on the cascade representations of this channel. Correspondingly, lower bounds on the error probability of communication over this channel are derived. Our results reveal that each bound may be preferred depending on the system parameters. Existing system: In this letter, we evaluate the capacity and performance of communication over the diffusion channel in the presence of the CPNS which we refer to as discrete-time
compound Poisson channel (DCPC). This diffusion channel model is different from the previously proposed models in the MC literature. In, additive inverse Gaussian noise distribution was developed for molecular timing channel and bounds on the capacity were obtained. In, Gaussian distribution was employed to characterize the noise of the diffusion channel. Another channel model which involves the uncertainity in both the release process of transmitter and Brownian motion is discrete-time Poisson channel. The key factor with discrete-time Poisson channel is that it suffers from a precise capacity expression. It is noteworthy to mention that although discrete-time Poisson channel is well known and studied in the classic communication systems both from communication and information theory aspects, but DCPC is introduced for the first time in based on our best of knowledge which requires to be evaluated from an information theoretic perspective. Proposed system: Bio-compatibility of DMC makes it very attractive for healthcare applications, where DMC system may face biological entities in the body which release different types of molecules as part of their functionality. Thereby, biological entities may play the role of external noise sources for the DMC system. The process of molecule release by a biological entity (biological noise source) is stochastic both for the time of release and the number of the released molecules. Inspired from the molecule release processes observed in some endocrine systems and the release of neurotransmitters in synapses, the release process of the biological noise source has been particularly modeled as a compound Poisson process (CPP) in, which is referred to as a compound Poisson noise source (CPNS) for the DMC system. Advantages: The released molecules move randomly via Brownian motion and, some molecules may be observed at the receiver. Bio-compatibility of DMC, makes it very attractive for healthcare applications], where DMC system may face biological entities in the body which release different types of molecules as part of their functionality.
Thereby, biological entities may play the role of external noise sources for the DMC system. The process of molecule release by a biological entity (biological noise source) is stochastic both for the time of release and the number of the released molecules. Disadvantages: In, Gaussian distribution was employed to characterize the noise of the diffusion channel. Another channel model which involves the uncertainity in both the release process of transmitter and Brownian motion is discrete-time Poisson channel. The key factor with discrete-time Poisson channel is that it suffers from a precise capacity expression. It is noteworthy to mention that although discrete-time Poisson channel is well known and studied in the classic communication systems both from communication and information theory aspects, but DCPC is introduced for the first time in based on our best of knowledge which requires to be evaluated from an information theoretic perspective. Modules: Molecular communication (DMC): Is envisioned as a promising approach for realizing nano networks. In DMC, information can be encoded in the concentration, type, and/or release time of molecules. The information molecules are released into the environment by the transmitter nano machine. The released molecules move randomly via Brownian motion and, some molecules may be observed at the receiver. Bio-compatibility of DMC makes it very attractive for healthcare applications, where DMC system may face biological entities in the body which release different types of molecules as part of their functionality. Thereby, biological entities may play the role of external noise sources for the DMC system. The process of molecule release by a biological entity (biological noise source) is stochastic both for the time of release and the number of the released molecules. Discrete – time compound Poisson channel:
Time events constitute points of a Poisson process and the amplitudes of the events (the number of released molecules at a release time event) are random. Noteworthy, the CPP model is incomprehensive and lacks to model all biological release processes in body. The output of point-to-point diffusion channel (receiver observation) in the presence of the CPNS coincides a discrete-time Poisson channel whose background noise rate is stochastic. Interestingly, the background noise rate is Gaussian distributed for the special case of CPNS with high rate of release time events. In this letter, we evaluate the capacity and performance of communication over the diffusion channel in the presence of the CPNS which we refer to as discrete-time compound Poisson channel (DCPC). This diffusion channel model is different from the previously proposed models in the MC literature. Additive inverse Gaussian noise: In, additive inverse Gaussian noise distribution was developed for molecular timing channel and bounds on the capacity were obtained. In, Gaussian distribution was employed to characterize the noise of the diffusion channel. Another channel model which involves the uncertainity in both the release process of transmitter and Brownian motion is discrete-time Poisson channel. The key factor with discrete-time Poisson channel is that it suffers from a precise capacity expression. It is noteworthy to mention that although discrete-time Poisson channel is well known and studied in the classic communication systems both from communication and information theory aspects, but DCPC is introduced for the first time in based on our best of knowledge which requires to be evaluated from an information theoretic perspective.