The Compression Optimality of Asymmetric Numeral Systems Article Swipe
Josef Pieprzyk
,
Jarek Duda
,
Marcin Pawłowski
,
Seyit Camtepe
,
Arash Mahboubi
,
Paweł Morawiecki
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3390/e25040672
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3390/e25040672
Source coding has a rich and long history. However, a recent explosion of multimedia Internet applications (such as teleconferencing and video streaming, for instance) renews interest in fast compression that also squeezes out as much redundancy as possible. In 2009 Jarek Duda invented his asymmetric numeral system (ANS). Apart from having a beautiful mathematical structure, it is very efficient and offers compression with a very low coding redundancy. ANS works well for any symbol source statistics, and it has become a preferred compression algorithm in the IT industry. However, designing an ANS instance requires a random selection of its symbol spread function. Consequently, each ANS instance offers compression with a slightly different compression ratio. The paper investigates the compression optimality of ANS. It shows that ANS is optimal for any symbol sources whose probability distribution is described by natural powers of 1/2. We use Markov chains to calculate ANS state probabilities. This allows us to precisely determine the ANS compression rate. We present two algorithms for finding ANS instances with a high compression ratio. The first explores state probability approximations in order to choose ANS instances with better compression ratios. The second algorithm is a probabilistic one. It finds ANS instances whose compression ratios can be made as close to the best ratio as required. This is done at the expense of the number θ of internal random “coin” tosses. The algorithm complexity is O(θL3), where L is the number of ANS states. The complexity can be reduced to O(θLlog2L) if we use a fast matrix inversion. If the algorithm is implemented on a quantum computer, its complexity becomes O(θ(log2L)3).
Related Topics
Concepts
Lossless compression
Data compression
Algorithm
Computer science
Data compression ratio
Compression (physics)
Redundancy (engineering)
Probabilistic logic
Compression ratio
Markov chain
Numeral system
Lossy compression
Theoretical computer science
Mathematics
Image compression
Artificial intelligence
Machine learning
Automotive engineering
Image (mathematics)
Materials science
Composite material
Internal combustion engine
Image processing
Operating system
Engineering
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/e25040672
- https://www.mdpi.com/1099-4300/25/4/672/pdf?version=1681732195
- OA Status
- gold
- Cited By
- 7
- References
- 38
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4366286491
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4366286491Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3390/e25040672Digital Object Identifier
- Title
-
The Compression Optimality of Asymmetric Numeral SystemsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-04-17Full publication date if available
- Authors
-
Josef Pieprzyk, Jarek Duda, Marcin Pawłowski, Seyit Camtepe, Arash Mahboubi, Paweł MorawieckiList of authors in order
- Landing page
-
https://doi.org/10.3390/e25040672Publisher landing page
- PDF URL
-
https://www.mdpi.com/1099-4300/25/4/672/pdf?version=1681732195Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
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-
https://www.mdpi.com/1099-4300/25/4/672/pdf?version=1681732195Direct OA link when available
- Concepts
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Lossless compression, Data compression, Algorithm, Computer science, Data compression ratio, Compression (physics), Redundancy (engineering), Probabilistic logic, Compression ratio, Markov chain, Numeral system, Lossy compression, Theoretical computer science, Mathematics, Image compression, Artificial intelligence, Machine learning, Automotive engineering, Image (mathematics), Materials science, Composite material, Internal combustion engine, Image processing, Operating system, EngineeringTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
7Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 4, 2024: 2, 2023: 1Per-year citation counts (last 5 years)
- References (count)
-
38Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.compression | 28, 61, 82, 107, 112, 118, 159, 172, 188, 202 |
| abstract_inverted_index.implemented | 261 |
| abstract_inverted_index.probability | 133, 178 |
| abstract_inverted_index.redundancy. | 67 |
| abstract_inverted_index.statistics, | 75 |
| abstract_inverted_index.applications | 15 |
| abstract_inverted_index.distribution | 134 |
| abstract_inverted_index.investigates | 116 |
| abstract_inverted_index.mathematical | 53 |
| abstract_inverted_index.Consequently, | 102 |
| abstract_inverted_index.probabilistic | 195 |
| abstract_inverted_index.O(θ(log2L)3). | 269 |
| abstract_inverted_index.approximations | 179 |
| abstract_inverted_index.probabilities. | 150 |
| abstract_inverted_index.teleconferencing | 18 |
| cited_by_percentile_year.max | 98 |
| cited_by_percentile_year.min | 89 |
| corresponding_author_ids | https://openalex.org/A5045977578 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 6 |
| corresponding_institution_ids | https://openalex.org/I1292875679, https://openalex.org/I4210087266, https://openalex.org/I42894916, https://openalex.org/I99542240 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/9 |
| sustainable_development_goals[0].score | 0.5299999713897705 |
| sustainable_development_goals[0].display_name | Industry, innovation and infrastructure |
| citation_normalized_percentile.value | 0.84720301 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |