IJPAM: Volume 89, No. 5 (2013)

ENTROPY BOUNDS USING ARITHMETIC-
GEOMETRIC-HARMONIC MEAN INEQUALITY

Om Parkash$^1$, Priyanka Kakkar$^2$
$^{1,2}$Department of Mathematics
Guru Nanak Dev University
Amritsar, 143005, INDIA


Abstract. In the present communication, we have developed new inequalities using arithmetic-geometric-harmonic mean inequality and consequently, applied our findings to the field of entropy theory. It is observed that our results provide the stronger upper bounds to Shannon entropy as found by Simic [10] and Tapus and Popescu [7] using Jensen's inequality. Moreover, we have extended our findings to the field of coding theory by providing the comparisons of various codeword lengths.

Received: September 12, 2013

AMS Subject Classification: 26B25, 94A17, 94A24, 94A29

Key Words and Phrases: entropy, arithmetic-geometric-harmonic mean inequality, decreasing function, Jensen's inequality, mean codeword length, probability distribution

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DOI: 10.12732/ijpam.v89i5.8 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 5