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We study the information leakage to a guessing adversary in zero-error sourcecoding. The source coding problem is defined by a confusion graph capturing thedistinguishability between source symbols. The information leakage is measuredby the ratio of the adversary's successful guessing probability after andbefore eavesdropping the codeword, maximized over all possible sourcedistributions. Such measurement under the basic adversarial model where theadversary makes a single guess and allows no distortion between its estimatorand the true sequence is known as the maximum min-entropy leakage or themaximal leakage in the literature. We develop a single-letter characterizationof the optimal normalized leakage under the basic adversarial model, togetherwith an optimum-achieving scalar stochastic mapping scheme. An interestingobservation is that the optimal normalized leakage is equal to the optimalcompression rate with fixed-length source codes, both of which can besimultaneously achieved by some deterministic coding schemes. We then extendthe leakage measurement to generalized adversarial models where the adversarymakes multiple guesses and allows certain level of distortion, for which wederive single-letter lower and upper bounds.

Information Leakage in Zero-Error Source Coding: A Graph-Theoretic Perspective