On Two-Stage Guessing
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Date
2021
Publication Type
Journal Article
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yes
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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 ρ-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 ρ-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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published
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Journal / series
Volume
12 (4)
Pages / Article No.
159
Publisher
MDPI
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Software
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Date collected
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Subject
guessing; majorization; method of types; Schur concavity; ranking function; Shannon entropy; Renyi entropy; Arimoto-Renyi conditional entropy
Organisational unit
03529 - Lapidoth, Amos / Lapidoth, Amos