P-adic arithmetic coding

TL;DR

This paper introduces a novel p-adic arithmetic coding algorithm that generalizes traditional arithmetic coding, offering incremental encoding and decoding based on p-adic numbers, with connections to Huffman and Golomb-Rice codes.

Contribution

The paper presents a new p-adic arithmetic coding algorithm that extends existing compression techniques and demonstrates its versatility and connections to well-known coding methods.

Findings

For p=2, it functions as an integer variant of arithmetic coding.

Under certain models, it produces Huffman codes.

For specific models and alphabets, it yields Golomb-Rice codes.

Abstract

A new incremental algorithm for data compression is presented. For a sequence of input symbols algorithm incrementally constructs a p-adic integer number as an output. Decoding process starts with less significant part of a p-adic integer and incrementally reconstructs a sequence of input symbols. Algorithm is based on certain features of p-adic numbers and p-adic norm. p-adic coding algorithm may be considered as of generalization a popular compression technique - arithmetic coding algorithms. It is shown that for p = 2 the algorithm works as integer variant of arithmetic coding; for a special class of models it gives exactly the same codes as Huffman's algorithm, for another special model and a specific alphabet it gives Golomb-Rice codes.