We consider decentralized detection through distributed sensors that perform level-triggered sampling and communicate with a fusion center via noisy channels. Each sensor computes its local log-likelihood ratio (LLR), samples it using the level-triggered sampling, and upon sampling transmits a single bit to the FC. Upon receiving a bit from a sensor, the FC updates the global LLR and performs a sequential probability ratio test (SPRT) step. We derive the fusion rules under various types of channels. We further provide an asymptotic analysis on the average detection delay for the proposed channel-aware scheme, and show that the asymptotic detection delay is characterized by a KL information number. The delay analysis facilitates the choice of appropriate signaling schemes under different channel types for sending the 1-bit information from sensors to the FC.