Greedy adaptive Fano coding

In this paper, we propose a greedy technique for adaptive Fano coding, which is suitable for a wide range of applications, specially those in which memory constraints are tight. Our scheme has great potential in maximizing the output entropy, and thus has also indirect cryptographic implications. This paper includes the encoding and decoding algorithms, and the partitioning procedures suitable for the binary and r-ary schemes. It also includes a rigorous analysis of the properties of the algorithm. Empirical results demonstrate that our adaptive Fano scheme compresses marginally less than the adaptive Huffman scheme. In terms of speed, the former is faster in the compression phase and slower in the decompression phase. We also present the extension of the binary adaptive Fano coding method to multi-symbol code alphabets. We introduce the corresponding partitioning procedure, which deals with consecutive partitionings that satisfy the principles of Fano coding. To find the optimal partitioning, we propose a brute force algorithm that searches the entire space of all possible partitionings in O(m^r-1) time. As opposed to this, we propose a greedy linear-time algorithm that finds a sub-optimal but accurate consecutive partitioning.