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In this paper, we analyze the asymptotics of the normalized remaininguncertainty of a source when a compressed or hashed version of it andcorrelated side-information is observed. For this system, commonly known asSlepian-Wolf source coding, we establish the optimal (minimum) rate ofcompression of the source to ensure that the remaining uncertainties vanish. Wealso study the exponential rate of decay of the remaining uncertainty to zerowhen the rate is above the optimal rate of compression. In our study, weconsider various classes of random universal hash functions. Instead ofmeasuring remaining uncertainties using traditional Shannon informationmeasures, we do so using two forms of the conditional R\'{e}nyi entropy. Amongother techniques, we employ new one-shot bounds and the moments of type classenumerator method for these evaluations. We show that these asymptotic resultsare generalizations of the strong converse exponent and the error exponent ofthe Slepian-Wolf problem under maximum \emph{a posteriori} (MAP) decoding.

Analysis of Remaining Uncertainties and Exponents under Various Conditional R\'{e}nyi Entropies