Cell signaling is essential for individual cells to execute various tasks and respond to changes in their environment. It is carried out via diffusing molecules, whose transport is often aided by directional advection. How diffusion and advection together impact the accuracy of information transmission during signaling remains poorly understood. Here, we study this problem using a simplified model of signal transport in the presence and absence of crowding. Mutual information, our measure of accuracy, shows three distinct regimes characterized by power-law decay. Surprisingly, crowding has no measurable effect on information transmission. Our results provide several important insights into the role of transport in cell signaling.