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Compression for exact match identification

In this paper, we consider the problem of determining whether sequences X and Y, generated i.i.d. according to P<sub>X</sub> × P<sub>Y</sub>, are equal given access only to the pair (Y, T(X)), where T(X) is a rate-R compressed version of X. In general, the rate R may not be sufficiently large to reliably determine whether X=Y. We precisely characterize this reliability - i.e., the exponential rate at which an error is made - as a function of R. Interestingly, the exponent turns out to be related to the Bhattacharyya distance between the distributions P<sub>X</sub> and P<sub>Y</sub>. In addition, the scheme achieving this exponent is universal, i.e. does not depend on P<sub>X</sub>, P<sub>Y</sub>.