Open AccessAnalysis of ripple size evolution in the LT process
Author(s) -
Khonsari Hossein,
Okpotse Toritseju,
Valipour Mehrdad,
Yousefi Shahram
Publication year - 2018
Publication title -
iet communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.355
H-Index - 62
eISSN - 1751-8636
pISSN - 1751-8628
DOI - 10.1049/iet-com.2017.1352
Subject(s) - ripple , decoding methods , expression (computer science) , algorithm , mathematics , computer science , closed form expression , function (biology) , topology (electrical circuits) , combinatorics , mathematical analysis , power (physics) , physics , biology , programming language , quantum mechanics , evolutionary biology
This study introduces a novel framework and analysis tool to monitor the evolution of the ripple size during the Luby‐transform (LT) decoding process. It provides a closed‐form probability expression to statistically describe the behaviour of the ripple size at each step of the decoding. The probability function is conditioned on the size of the ripple in the previous step, the number of recovered source symbols and the encoded symbols' degree distribution. The authors further derive a closed‐form expression for the ripple size after new encoded symbols are received by a decoder with an empty ripple. This relates to the activation of belief propagation decoding attempts once premature terminations occur. They validate their analyses through numerical examples of an LT‐coded system. The results show that their analyses precisely coincide with the numerical results.