On the Impact of Transposition Errors in Diffusion-Based Channels

In this paper, we consider diffusion-based molecular communication with and without drift between two static nano-machines. We employ type-based information encoding, releasing a single molecule per information bit. At the receiver, we consider an asynchronous detection algorithm which exploits the arrival order of the molecules. In such systems, transposition errors fundamentally undermine reliability and capacity. Thus, in this paper, we study the impact of transpositions on the system performance. Toward this, we present an analytical expression for the exact bit error probability (BEP) caused by transpositions and derive computationally tractable approximations of the BEP for diffusion-based channels with and without drift. Based on these results, we analyze the BEP when background is not negligible and derive the optimal bit interval that minimizes the BEP. Simulation results confirm the theoretical results and show the error and goodput performance for different parameters such as block size or noise generation rate.