The Twelvefold Way of Non-Sequential Lossless Compression
Many information sources are not just sequences of distinguishable symbols but rather have invariances governed by alternative counting paradigms such as permutations, combinations, and partitions. We consider an entire classification of these invariances called the twelvefold way in enumerative com...
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| creator | Taha Ameen ur Rahman Barbehenn, Alton S Chen, Xinan Dbouk, Hassan Douglas, James A Geng, Yuncong George, Ian Harvill, John B Sung Woo Jeon Kansal, Kartik K Lee, Kiwook Levick, Kelly A Li, Bochao Li, Ziyue Murthy, Yashaswini Muthuveeru-Subramaniam, Adarsh Olmez, S Yagiz Tomei, Matthew J Veeravalli, Tanya Wang, Xuechao Wayman, Eric A Wu, Fan Xu, Peng Shen, Yan Zhang, Heling Zhang, Yibo Zhang, Yifan Zhao, Yibo Basu, Sourya Varshney, Lav R |
| description | Many information sources are not just sequences of distinguishable symbols but rather have invariances governed by alternative counting paradigms such as permutations, combinations, and partitions. We consider an entire classification of these invariances called the twelvefold way in enumerative combinatorics and develop a method to characterize lossless compression limits. Explicit computations for all twelve settings are carried out for i.i.d. uniform and Bernoulli distributions. Comparisons among settings provide quantitative insight. |
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| subjects | Combinations (mathematics) Combinatorial analysis Information sources Permutations |
| title | The Twelvefold Way of Non-Sequential Lossless Compression |
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