Large deviations for conditional guesswork

Abstract

The guesswork problem was originally studied by Massey to quantify the number of guesses needed to ascertain a discrete random variable. It has been shown that for a large class of random processes the rescaled logarithm of the guesswork satisfies the large deviation principle and this has been extended to the case where $k$ out $m$ sequences are guessed. The study of conditional guesswork, where guessing of a sequence is aided by the observation of another one, was initiated by Ar{\i}kan in his simple derivation of the upper bound of the cutoff rate for sequential decoding. In this note, we extend these large deviation results to the setting of conditional guesswork.