TY - JOUR

T1 - On the Use of Variability Measures to Analyze Source Coding Data Based on the Shannon Entropy

AU - de Oliveira, Helio M.

AU - Ospina, Raydonal

AU - Martin-Barreiro, Carlos

AU - Leiva, Víctor

AU - Chesneau, Christophe

N1 - Publisher Copyright:
© 2023 by the authors.

PY - 2023/1

Y1 - 2023/1

N2 - Source coding maps elements from an information source to a sequence of alphabetic symbols. Then, the source symbols can be recovered exactly from the binary units. In this paper, we derive an approach that includes information variation in the source coding. The approach is more realistic than its standard version. We employ the Shannon entropy for coding the sequences of a source. Our approach is also helpful for short sequences when the central limit theorem does not apply. We rely on a quantifier of the information variation as a source. This quantifier corresponds to the second central moment of a random variable that measures the information content of a source symbol; that is, considering the standard deviation. An interpretation of typical sequences is also provided through this approach. We show how to use a binary memoryless source as an example. In addition, Monte Carlo simulation studies are conducted to evaluate the performance of our approach. We apply this approach to two real datasets related to purity and wheat prices in Brazil.

AB - Source coding maps elements from an information source to a sequence of alphabetic symbols. Then, the source symbols can be recovered exactly from the binary units. In this paper, we derive an approach that includes information variation in the source coding. The approach is more realistic than its standard version. We employ the Shannon entropy for coding the sequences of a source. Our approach is also helpful for short sequences when the central limit theorem does not apply. We rely on a quantifier of the information variation as a source. This quantifier corresponds to the second central moment of a random variable that measures the information content of a source symbol; that is, considering the standard deviation. An interpretation of typical sequences is also provided through this approach. We show how to use a binary memoryless source as an example. In addition, Monte Carlo simulation studies are conducted to evaluate the performance of our approach. We apply this approach to two real datasets related to purity and wheat prices in Brazil.

KW - Monte Carlo simulation

KW - Newton–Raphson method

KW - communication science

KW - discrete memoryless source

KW - entropy

KW - information theory

KW - statistical moments

KW - variance

UR - http://www.scopus.com/inward/record.url?scp=85146795021&partnerID=8YFLogxK

U2 - 10.3390/math11020293

DO - 10.3390/math11020293

M3 - Article

AN - SCOPUS:85146795021

SN - 2227-7390

VL - 11

JO - Mathematics

JF - Mathematics

IS - 2

M1 - 293

ER -