On the Capacity of the Joint Time and Concentration Modulation for Molecular Communications

Abstract: Most diffusion based molecular channels suffer from low information capacity due to the structure of the diffusion environment. To address this issue, this paper studies the capacity of the diffusion based molecular communication by exploiting both time and concentration level of the released molecules for information transfer. The transmitter releases molecules in one of the sub-intervals with a level of concentration both determined by input data, hereby applying joint time and concentration (JTAC) modulation. The observation time, at the receiver, which is equal to symbol period, is divided to some sub-intervals, not necessarily equal to the number of sub-intervals in the transmitter, and the number of received molecules in each sub-interval is counted. We propose three practical schemes, depending on how the receiver uses the number of molecules counted in the sub-intervals and find the lower bound on capacity in each case. Moreover, the symmetric Kullback-Liebler (KL) divergence metric is used to obtain a computable upper bound on the JTAC channel capacity. Finally, the Blahut-Arimoto algorithm is used to compute the capacity numerically, and to determine how tight the derived bounds are. Our numerical results indicate that our bounds are tight especially in environments with high diffusion coefficient. The improvements compared to the conventional concentration based modulation and timing based modulation are also demonstrated.