Fair Numerical Algorithm of Coset Cardinality Spectrum for Distributed Arithmetic Coding
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 r...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/25/3/437 |
| _version_ | 1827749892243587072 |
|---|---|
| author | Yong Fang Nan Yang |
| author_facet | Yong Fang Nan Yang |
| author_sort | Yong Fang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T06:34:56Z |
| format | Article |
| id | doaj.art-630ab99e8078497593cb9c1c8ea86778 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T06:34:56Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-630ab99e8078497593cb9c1c8ea867782023-11-17T10:56:11ZengMDPI AGEntropy1099-43002023-03-0125343710.3390/e25030437Fair Numerical Algorithm of Coset Cardinality Spectrum for Distributed Arithmetic CodingYong Fang0Nan Yang1School of Information Engineering, Chang’an University, Xi’an 710064, ChinaSchool of Information Engineering, Chang’an University, Xi’an 710064, ChinaAs 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.https://www.mdpi.com/1099-4300/25/3/437distributed arithmetic codingSlepian-Wolf codingcoset cardinality spectrumnumerical algorithm |
| spellingShingle | Yong Fang Nan Yang Fair Numerical Algorithm of Coset Cardinality Spectrum for Distributed Arithmetic Coding Entropy distributed arithmetic coding Slepian-Wolf coding coset cardinality spectrum numerical algorithm |
| title | Fair Numerical Algorithm of Coset Cardinality Spectrum for Distributed Arithmetic Coding |
| title_full | Fair Numerical Algorithm of Coset Cardinality Spectrum for Distributed Arithmetic Coding |
| title_fullStr | Fair Numerical Algorithm of Coset Cardinality Spectrum for Distributed Arithmetic Coding |
| title_full_unstemmed | Fair Numerical Algorithm of Coset Cardinality Spectrum for Distributed Arithmetic Coding |
| title_short | Fair Numerical Algorithm of Coset Cardinality Spectrum for Distributed Arithmetic Coding |
| title_sort | fair numerical algorithm of coset cardinality spectrum for distributed arithmetic coding |
| topic | distributed arithmetic coding Slepian-Wolf coding coset cardinality spectrum numerical algorithm |
| url | https://www.mdpi.com/1099-4300/25/3/437 |
| work_keys_str_mv | AT yongfang fairnumericalalgorithmofcosetcardinalityspectrumfordistributedarithmeticcoding AT nanyang fairnumericalalgorithmofcosetcardinalityspectrumfordistributedarithmeticcoding |