  We consider the problem of recovering the rank of a set of $n$ items based on
noisy pairwise comparisons. We assume the SST class as the family of generative
models. Our analysis gave sharp information theoretic upper and lower bound for
the exact requirement, which matches exactly in the parametric limit. Our tight
analysis on the algorithm induced by the moment method gave better constant in
Minimax optimal rate than ~\citet{shah2017simple} and contribute to their open
problem. The strategy we used in this work to obtain information theoretic
bounds is based on combinatorial arguments and is of independent interest.
