Mixed $d$-Ary Fibonacci Codes

We propose a family of Fibonacci-style codes, combining the advantages of higher-order Fibonacci numeration systems and the flexibility of binary mixed-digit codes. We establish the theoretical foundation of these new codes, proving a generalization of the Kraft inequality for prefix-free codes on mixed-digit numeration systems and the completeness of the new family of Fibonacci codes. Experiments on natural language text show that the proposed codes provide a coding structure that can adapt to various data distributions and capable of achieving superior compression ratios.