Fair Numerical Algorithm of Coset Cardinality Spectrum for Distributed Arithmetic Coding

• Published in: Entropy (Basel, Switzerland) Vol. 25; no. 3; p. 437
• Main Authors: Fang, Yong, Yang, Nan
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 01.03.2023; MDPI
• Subjects: Algorithms; Arithmetic coding; Codes; Coding theory; coset cardinality spectrum; Data compression; distributed arithmetic coding; Distributions, Theory of (Functional analysis); Mathematical research; Numbers, Cardinal; numerical algorithm; Numerical analysis; Random variables; Slepian-Wolf coding; China; distributed arithmetic coding; Slepian-Wolf coding; numerical algorithm; coset cardinality spectrum
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e25030437

As a typical symbol-wise solution of asymmetric Slepian-Wolf coding problem, Distributed Arithmetic Coding (DAC) non-linearly partitions source space into disjoint cosets with unequal sizes. The distribution of DAC coset cardinalities, named the Coset Cardinality Spectrum (CCS), plays an important role in both theoretical understanding and decoder design for DAC. In general, CCS cannot be calculated directly. Instead, a numerical algorithm is usually used to obtain an approximation. This paper first finds that the contemporary numerical algorithm of CCS is theoretically imperfect and does not finally converge to the real CCS. Further, to solve this problem, we refine the original numerical algorithm based on rigorous theoretical analyses. Experimental results verify that the refined numerical algorithm amends the drawbacks of the original version.