Capacity of LTI-Poisson channel for diffusion based molecular communication

The LTI-Poisson model is a natural extension of the conventional memoryless Poisson channel to include memory, and can model the ISI effect in diffusion based molecular communication networks. In this paper, we exploit prior art on linear ISI channels to provide a computable finite-letter characterization of the capacity of single-hop LTI-Poisson networks. Then we find more explicit single-letter lower and upper bounds on the capacity in the point to point case. Further, an approach for bounding mutual information in the low SNR regime using the symmetrized KL divergence is introduced and its applicability for Poisson channels is demonstrated. This leads to a non-trivial upper bound on the capacity of Poisson channel with a maximum transmission constraint in the low SNR regime, which to best of our knowledge is the first such bound.