In this paper, the capacity of a diffusion-based molecular communication network under the model of a Linear Time Invariant-Poisson (LTI-Poisson) channel is studied. Introduced in the context of molecular communication, the LTI-Poisson model is a natural extension of the conventional memoryless Poisson channel to include memory. Exploiting prior art on linear intersymbol interference (ISI) channels, a computable finite-letter characterization of the capacity of single-hop LTI-Poisson networks is provided. Then, the problem of finding more explicit bounds on the capacity is examined, where lower and upper bounds for the point to point case are provided. Furthermore, an approach for bounding mutual information in the low SNR regime using the symmetrized KL divergence is introduced and its applicability to Poisson channels is shown. To the best of our knowledge, the first upper bound on the capacity of Poisson channel with a maximum transmission constraint in the low SNR regime is found. Numerical results show that the proposed upper bound is of the same order as the capacity in the low SNR regime.
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