Multidimensional Fibonacci Coding
Issued Date
2022-02-01
Resource Type
eISSN
22277390
Scopus ID
2-s2.0-85123572309
Journal Title
Mathematics
Volume
10
Issue
3
Rights Holder(s)
SCOPUS
Bibliographic Citation
Mathematics Vol.10 No.3 (2022)
Suggested Citation
Pooksombat P., Udomkavanich P., Kositwattanarerk W. Multidimensional Fibonacci Coding. Mathematics Vol.10 No.3 (2022). doi:10.3390/math10030386 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/87536
Title
Multidimensional Fibonacci Coding
Author(s)
Other Contributor(s)
Abstract
Fibonacci codes are self-synchronizing variable-length codes that are proven useful for their robustness and compression capability. Asymptotically, these codes provide better compression efficiency as the order of the underlying Fibonacci sequence increases but at the price of the increased suffix length. We propose a circumvention to this problem by introducing higher-dimensional Fibonacci codes for integer vectors. The resulting multidimensional Fibonacci coding is comparable to the classical one in terms of compression; while encoding several numbers all at once for a shared suffix generally results in a shorter codeword, the efficiency takes a backlash when terms from different orders of magnitude are encoded together. In addition, while laying the groundwork for the new encoding scheme, we provide extensive theoretical background and generalize the theorem of Zeckendorf to higher order. As such, our work unifies several variations of Zeckendorf’s theorem while also providing new grounds for its legitimacy.