Abstract
In this paper, we study the zero error capacity of the molecular delay channel when multiple molecule types are available at the transmitter. In the molecular delay channel, each transmitted molecule (of any type) is received by a delay of at most k time slots. Depending on the number of molecules that the transmitter is allowed to release in each time slot, we consider the following three cases: (i) when the maximum number of the released molecules of each type in each time slot is restricted (ii) when the total number of the released molecules (regardless of their type) in each time slot is restricted, and (iii) when the transmitter can use only one molecule type (of its choice) in each time slot. We derive lower bounds on the zero-error capacity of the delay channel for each case, by proposing zero-error codes that are based on the results by Kovačević and Popovski. We also derive upper bounds on the zero-error capacity of the delay channel. In the first case, these bounds match and yield the exact capacity, while in the other two cases, the bounds are shown to be close numerically. Our numerical results show that as the number of available molecule types increases, the capacity of the system increases substantially, compared to using only one molecule type. Furthermore, it is shown that the lower and upper bounds on the zero-error capacity of the delay channel in the second case are generally close to the lower and upper bounds in the third case, respectively, indicating the closeness of the zero-error capacities of the two cases. This result enables one to design a simpler system by employing a high rate code that has only one molecule type in each slot (designed for the third case) in the channel of the second case, without much rate loss.