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

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 ${\mathbb{Z}}_{\ge 0}^d$ to the entropy, in the limit.

9 pages, 4 figures, 3 algorithms