The Twelvefold Way of Non-Sequential Lossless Compression
Information Theory
2021-01-21 v2 math.IT
Abstract
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.
Cite
@article{arxiv.2011.04069,
title = {The Twelvefold Way of Non-Sequential Lossless Compression},
author = {Taha Ameen ur Rahman and Alton S. Barbehenn and Xinan Chen and Hassan Dbouk and James A. Douglas and Yuncong Geng and Ian George and John B. Harvill and Sung Woo Jeon and Kartik K. Kansal and Kiwook Lee and Kelly A. Levick and Bochao Li and Ziyue Li and Yashaswini Murthy and Adarsh Muthuveeru-Subramaniam and S. Yagiz Olmez and Matthew J. Tomei and Tanya Veeravalli and Xuechao Wang and Eric A. Wayman and Fan Wu and Peng Xu and Shen Yan and Heling Zhang and Yibo Zhang and Yifan Zhang and Yibo Zhao and Sourya Basu and Lav R. Varshney},
journal= {arXiv preprint arXiv:2011.04069},
year = {2021}
}
Comments
DCC 2021