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This paper investigates the fault-diagnosis problem for all-optical wavelength-division-multiplexing (WDM) networks. A family of failure-localization algorithms that exploit the unique properties of all-optical networks is proposed. Optical probe signals are sequentially sent along a set of designed lightpaths, and the network state is inferred from the result of this set of end-to-end measurements. The design objective is to minimize the diagnosis effort (e.g., the average number of probes) to locate failures. By establishing a mathematical equivalence between the fault-diagnosis problem and the source-coding problem in information theory, we obtain a tight lower bound for the minimum average number of probes per edge (of the network modeled as a graph) as Hb(p), the entropy of the individual edges. Using the rich set of results from coding theory to solve the fault-diagnosis problem, it is shown that the "2m-splitting" probing scheme is optimum for the special case of single failure over a linear network. A class of near-optimum run-length probing schemes that have low computation complexity is then developed. Analytical and numerical results suggest that the average number of probes per edge for the run-length probing scheme is uniformly bounded above by (1+ε)Hb(p) and converges to the entropy lower bound as the failure probability decreases. From an information-theoretic perspective, it is shown that the run-length probing scheme outperforms the greedy probing scheme of the same computational complexity. The investigation reveals a guideline for efficient fault-diagnosis schemes: Each probe should provide approximately 1 bit of information, and the total number of probes required is approximately equal to the entropy of the state of the network. This result provides an insightful guideline to reduce the overhead cost of fault management for all-optical networks and can further the understanding of the relationship between information entropy and network management. Several practical issues are also addressed in the implementation of run-length probing schemes over all-optical WDM networks.