The exact reconstruction threshold for the three-state symmetric channel
We determine the exact reconstruction threshold for the symmetric three-state broadcast process on every regular b -ary tree, b ≥ 2, and every observed Poisson Galton–Watson tree of mean d > 1. Reconstruction occurs exactly when $d\lambda^2\gt 1$, with d = b in the regular model; there is non-reconstruction at equality for either sign of the channel parameter. The Poisson advantage is averaged over trees and spins without conditioning on survival. This resolves the all-degree three-state regular-tree prediction. Combining the Poisson theorem with known tree-to-graph and algorithmic results…
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