TY - GEN
T1 - Exact Expressions in Source and Channel Coding Problems Using Integral Representations
AU - Merhav, Neri
AU - Sason, Igal
N1 - Publisher Copyright: © 2020 IEEE.
PY - 2020/6
Y1 - 2020/6
N2 - 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 ρ>0 of a non-negative random variable (or the sum of i.i.d. positive 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 Rényi 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).
AB - 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 ρ>0 of a non-negative random variable (or the sum of i.i.d. positive 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 Rényi 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).
UR - http://www.scopus.com/inward/record.url?scp=85090412929&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/ISIT44484.2020.9174294
DO - https://doi.org/10.1109/ISIT44484.2020.9174294
M3 - منشور من مؤتمر
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2343
EP - 2348
BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
T2 - 2020 IEEE International Symposium on Information Theory, ISIT 2020
Y2 - 21 July 2020 through 26 July 2020
ER -