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We study error exponents for the problem of low-rate communication over adirected graph, where each edge in the graph represents a noisy communicationchannel, and there is a single source and destination. We derive maxflow-basedachievability and converse bounds on the error exponent that match when thereare two messages and all channels satisfy a symmetry condition called pairwisereversibility. More generally, we show that the upper and lower bounds match towithin a factor of 4. We also show that with three messages there are caseswhere the maxflow-based error exponent is strictly suboptimal, thus showingthat our tightness result cannot be extended beyond two messages withoutfurther assumptions.

Maxflow-Based Bounds for Low-Rate Information Propagation over Noisy Networks