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• W3100404149 abstract "We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily computable exact formulas for quantities that involve expectations and higher moments of the logarithm of a positive random variable (or the logarithm of a sum of i.i.d. positive random variables). The integral representation of the logarithm is proved useful in a variety of information-theoretic applications, including universal lossless data compression, entropy and differential entropy evaluations, and the calculation of the ergodic capacity of the single-input, multiple-output (SIMO) Gaussian channel with random parameters (known to both transmitter and receiver). This integral representation and its variants are anticipated to serve as a useful tool in additional applications, as a rigorous alternative to the popular (but non-rigorous) replica method (at least in some situations)." @default.
• W3100404149 created "2020-11-23" @default.
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• W3100404149 date "2019-12-30" @default.
• W3100404149 modified "2023-09-26" @default.
• W3100404149 title "An Integral Representation of the Logarithmic Function with Applications in Information Theory" @default.
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• W3100404149 doi "https://doi.org/10.3390/e22010051" @default.
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