  In this work, 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 work we study
the impact of transpositions on the system performance. Towards 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.
