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Motivated by the spatiotemporal waves of MAPK/ERK activity, crucial for long-range communication in regenerating tissues, we investigated stochastic homoclinic fronts propagating through channels formed by directly interacting cells. We evaluated the efficiency of long-range communication in these channels by examining the rate of information transmission. Our study identified the stochastic phenomena that reduce this rate: front propagation failure, new front spawning, and variability in the front velocity. We found that a trade-off between the frequencies of propagation failures and new front spawning determines the optimal channel width (which geometrically determines the front length). The optimal frequency of initiating new waves is determined by a trade-off between the input information rate (higher with more frequent initiation) and the fidelity of information transmission (lower with more frequent initiation). Our analysis provides insight into the relative timescales of intra- and intercellular processes necessary for successful wave propagation.