On the Input-Output Relationship for Molecular Communications in General First-Order Chemical Reaction-Diffusion Systems

Malcolm Egan 1, 2 Tang Quoc Bao 3 Bayram Cevdet Akdeniz 1, 2
1 MARACAS - Modèle et algorithmes pour des systèmes de communication fiables
Inria Grenoble - Rhône-Alpes, CITI - CITI Centre of Innovation in Telecommunications and Integration of services
2 CITI - CITI Centre of Innovation in Telecommunications and Integration of services
3 University of Graz
Abstract : Any general model for a molecular communication system must account for both chemical reactions and diffusion. In particular, the chemical reactions capture processes of information molecule production and detection as well as inter-symbol mitigation methods in the channel. A popular model for such reaction-diffusion systems is the reaction-diffusion master equation. In this paper, we study the statistics for the number of molecules at the receiver, yielding a stochastic input-output relationship. Our focus is on a general class of first-order reactions and linear diffusion. This class of models admits a stationary distribution for the long-term behavior. We obtain a simple Gaussian approximation for this stationary distribution by exploiting recent results characterizing the underlying deterministic reaction-diffusion system. We prove exponential rates of convergence in the underlying deterministic system and verify our approximation via stochastic simulation.
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Malcolm Egan, Tang Quoc Bao, Bayram Cevdet Akdeniz. On the Input-Output Relationship for Molecular Communications in General First-Order Chemical Reaction-Diffusion Systems. NanoCom 2019 - Sixth Annual ACM International Conference on Nanoscale Computing and Communication, Sep 2019, Dublin, Ireland. pp.1-6, ⟨10.1145/3345312.3345477⟩. ⟨hal-02304088⟩

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