An Information Theoretic Approach to Probability Mass Function Truncation

Cicalese, Ferdinando; Gargano, Luisa; Vaccaro, Ugo

doi:10.1109/isit.2019.8849355

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Algorithm 3 (Construction Of the Pmf1

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2021

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“…Algorithm 3 was introduced in [26,28]. The link between the Rényi entropy of X m and that of Y * was given in Equation (34) of [14]:…”

Section: Algorithm 3 (Construction Of the Pmfmentioning

confidence: 99%

On Two-Stage Guessing

Graczyk

Sason

2021

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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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“…Algorithm 3 was introduced in [26,28]. The link between the Rényi entropy of X m and that of Y * was given in Equation (34) of [14]:…”

Section: Algorithm 3 (Construction Of the Pmfmentioning

confidence: 99%