This paper studies collusion in an infinitely repeated game when the opponent's past actions are observed only through a noisy public signal. Attention is focused on a threshold strategy, which switches between cooperation and punishment phases based on the comparison between the realized public signal and a threshold. The paper identifies sufficient conditions for such a strategy to support the most efficient symmetric (perfect public) equilibrium, and characterizes its payoff as a function of noise in monitoring. The theoretical predictions are then tested in laboratory experiments. It is found that subjects' payoffs (i) decrease as noise increases, and (ii) are lower than the theoretical maximum for small noise, but exceed it for large noise. It is also estimated that the subjects' strategies are best described by a simple threshold strategy that looks only at the most recent public signal.