Technical Program

Paper Detail

Paper IDS.13.3
Paper Title Exact Expressions in Source and Channel Coding Problems Using Integral Representations
Authors Neri Merhav, Igal Sason, Technion - Israel Institute of Technology, Israel
Session S.13: Topics in Shannon Theory
Presentation Lecture
Track Shannon Theory
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Abstract We explore known integral representations of the logarithmic and power functions, and demonstrate their usefulness for information-theoretic analyses. We obtain compact, easily--computable exact formulas for several source and channel coding problems that involve expectations and higher moments of the logarithm of a positive random variable and the moment of order $\rho > 0$ of a non-negative random variable (or the sum of such i.i.d. random variables). These integral representations are used in a variety of applications, including the calculation of the degradation in mutual information between the channel input and output as a result of jamming, universal lossless data compression, Shannon and R\'{e}nyi entropy evaluations, and the ergodic capacity evaluation of the single-input, multiple--output (SIMO) Gaussian channel with random parameters (known to both transmitter and receiver). The integral representation of the logarithmic function and its variants are anticipated to serve as a rigorous alternative to the popular (but non--rigorous) replica method (at least in some situations).

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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