# Multidimensional Fibonacci Coding

## TL;DR

This paper introduces higher-dimensional Fibonacci codes for integer vectors, generalizing Zeckendorf's theorem, to improve compression efficiency while addressing suffix length issues in traditional Fibonacci coding.

## Contribution

It proposes a novel multidimensional Fibonacci coding scheme and extends Zeckendorf's theorem to higher orders, unifying various existing code variations.

## Key findings

- Theoretical foundation for multidimensional Fibonacci codes
- Generalization of Zeckendorf's theorem to higher dimensions
- Potential for improved compression efficiency

## 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. In the process, we provide extensive theoretical background and generalize the theorem of Zeckendorf to higher order. As thus, our work unify several variations of Zeckendorf's theorem while also providing new grounds for its legitimacy.