On Jacob Ziv's Individual-Sequence Approach to Information Theory

TL;DR

This paper honors Jacob Ziv's pioneering individual-sequence approach and the Lempel-Ziv algorithm, highlighting their broad impact on information theory, data compression, and various problem domains, reflecting on their technical power and legacy.

Contribution

It emphasizes the significance and versatility of Ziv's individual-sequence approach and the LZ algorithm across multiple areas in information theory and beyond.

Findings

LZ algorithm's broad utility in data compression and other fields

The foundational role of Ziv's approach in shaping information theory

The enduring influence of Ziv's work on current research

Abstract

This article stands as a tribute to the enduring legacy of Jacob Ziv and his landmark contributions to information theory. Specifically, it delves into the groundbreaking individual-sequence approach -- a cornerstone of Ziv's academic pursuits. Together with Abraham Lempel, Ziv pioneered the renowned Lempel-Ziv (LZ) algorithm, a beacon of innovation in various versions. Beyond its original domain of universal data compression, this article underscores the broad utility of the individual-sequence approach and the LZ algorithm across a wide spectrum of problem areas. As we traverse through the forthcoming pages, it will also become evident how Ziv's visionary approach has left an indelible mark on my own research journey, as well as on those of numerous colleagues and former students. We shall explore, not only the technical power of the LZ algorithm, but also its profound impact on shaping the landscape of information theory and its applications.