Multidimensional Fibonacci Coding

Fibonacci codes are self-synchronizing variable-length that proven useful for their robustness and compression capability. Asymptotically, these provide better efficiency as the order of underlying sequence increases but at price increased suffix length. We propose a circumvention to this problem by introducing higher-dimensional integer vectors. The resulting multidimensional coding is comparable classical one in terms compression; while encoding several numbers all once shared generally results shorter codeword, takes backlash when from different orders magnitude encoded together. In addition, laying groundwork new scheme, we extensive theoretical background generalize theorem Zeckendorf higher order. As such, our work unifies variations Zeckendorf’s also providing grounds its legitimacy.