Abstract
Stationary memoryless sources produce two correlated random sequences $Xn$ and $Yn$. A guesser seeks to recover $Xn$ in two stages, by first guessing $Yn$ and then $Xn$. The contributions of this work are twofold: (1) We characterize the least achievable exponential growth rate (in $n$) of any positive $\rho$-th moment of the total number of guesses when $Yn$ is obtained by applying a deterministic function $f$ component-wise to $Xn$. We prove that, depending on $f$, the least exponential growth rate in the two-stage setup is lower than when guessing $Xn$ directly. We further propose a simple Huffman code-based construction of a function $f$ that is a viable candidate for the minimization of the least exponential growth rate in the two-stage guessing setup. (2) We characterize the least achievable exponential growth rate of the $\rho$-th moment of the total number of guesses required to recover $Xn$ when Stage 1 need not end with a correct guess of $Yn$ and without assumptions on the stationary memoryless sources producing $Xn$ and $Yn$.
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