Achievable Rate Analysis in Diffusive Molecular Communication Channels with Memory

In this paper, we investigate the achievable rate of a diffusive Molecular Communication (MC) channel with a fully absorbing (FA) receiver. The FA receiver counts the number of particles absorbed along each symbol interval and resets the counter at every interval. The MC channel is affected by a memory effect due to the delayed arrival of molecules, and therefore inter-symbol interference (ISI) arises. To quantify ISI we provide a measure of the effective channel memory, which is given in terms of integer number of symbol intervals. Thus, in our model the effect of released particles remains effective for a limited number of symbol intervals. The channel includes a single-sample memoryless detector, which is the most simple and common form of detector. We optimize the detector threshold to maximize the mutual information (MI), approximate as Gaussian the received signal distribution, and calculate the MI affected by ISI, in the case of binary concentration shift keying modulation. Our results demonstrate that, in general, the optimal input probability distribution that maximizes the achievable rate may not be uniform. In particular, when the symbol interval is small (strong ISI), the maximum achievable rate does not occur with equiprobable transmission of symbols.