Sequential Recurrence-Based Multidimensional Universal Source Coding of Lempel-Ziv Type

TL;DR

This paper introduces a sequential multidimensional source coding algorithm that efficiently compresses ergodic processes by parsing arrays into nested sub-arrays, achieving near-entropy compression in the limit.

Contribution

It presents a novel multidimensional universal source coding method based on recurrence, extending Lempel-Ziv type algorithms to higher dimensions.

Findings

Compresses almost all ergodic array realizations to entropy limit

Uses nested sub-array parsing for efficient coding

Achieves asymptotic optimality in multidimensional settings

Abstract

We define an algorithm that parses multidimensional arrays sequentially into mainly unrepeated but nested multidimensional sub-arrays of increasing size, and show that the resulting sub-block pointer encoder compresses almost every realization of any finite-alphabet ergodic process on $\mathbb{Z}_{\geq0}^d$ to the entropy, in the limit.