Generalized Universal Coding of Integers
Wei Yan, Sian-Jheng Lin, Yunghsiang S. Han

TL;DR
This paper introduces generalized universal coding of integers (GUCI), which ensures the expected codeword length remains within a constant factor of the Shannon entropy, addressing limitations of traditional universal integer coding.
Contribution
The paper defines GUCI, proposes a coding structure, and demonstrates its optimality and advantages over existing UCI, especially when entropy is small or zero.
Findings
GUCI achieves a constant factor bound to H(P)
Optimal GUCI has expansion factor between 1 and 2
GUCI can produce shorter codes than UCI in certain cases
Abstract
Universal coding of integers~(UCI) is a class of variable-length code, such that the ratio of the expected codeword length to is within a constant factor, where is the Shannon entropy of the decreasing probability distribution . However, if we consider the ratio of the expected codeword length to , the ratio tends to infinity by using UCI, when tends to zero. To solve this issue, this paper introduces a class of codes, termed generalized universal coding of integers~(GUCI), such that the ratio of the expected codeword length to is within a constant factor . First, the definition of GUCI is proposed and the coding structure of GUCI is introduced. Next, we propose a class of GUCI to achieve the expansion factor and show that the optimal GUCI is in the range . Then, by…
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · DNA and Biological Computing
