Related papers: Lempel-Ziv: a "one-bit catastrophe" but not a trag…
We study the sensitivity of the Lempel-Ziv 77 compression algorithm to edits, showing how modifying a string $w$ can deteriorate or improve its compression. Our first result is a tight upper bound for $k$ edits: $\forall w' \in B(w,k)$, we…
A bit catastrophe, loosely defined, is when a change in just one character of a string causes a significant change in the size of the compressed string. We study this phenomenon for the Burrows-Wheeler Transform (BWT), a string transform at…
A finite word $w$ is called \textit{closed} if it has length at most 1 or it contains a proper factor that occurs both as a prefix and as a suffix but does not have internal occurrences in $w$. An infinite word $u$ is called…
The complexity function of an infinite word $w$ on a finite alphabet $A$ is the sequence counting, for each non-negative $n$, the number of words of length $n$ on the alphabet $A$ that are factors of the infinite word $w$. For any given…
One of the most famous and investigated lossless data-compression scheme is the one introduced by Lempel and Ziv about 40 years ago. This compression scheme is known as "dictionary-based compression" and consists of squeezing an input…
The paper proposes an improved error-resilient Lempel-Ziv'77 (LZ'77) algorithm employing an adaptive amount of parity bits for error protection. It is a modified version of error resilient algorithm LZRS'77, proposed recently, which uses a…
The sensitivity of a string compression algorithm $C$ asks how much the output size $C(T)$ for an input string $T$ can increase when a single character edit operation is performed on $T$. This notion enables one to measure the robustness of…
We present a simple adaptation of the Lempel Ziv 78' (LZ78) compression scheme ({\em IEEE Transactions on Information Theory, 1978}) that supports efficient random access to the input string. Namely, given query access to the compressed…
The unrestricted LZ78 universal data-compression algorithm (as well as the LZ77 and LZW versions) achieves asymptotically, as the block-length tends to infinity, the FS compressibility, namely the best compression-ratio that may be achieved…
We show how to compress string dictionaries using the Lempel-Ziv (LZ78) data compression algorithm. Our approach is validated experimentally on dictionaries of up to 1.5 GB of uncompressed text. We achieve compression ratios often…
For any infinite word $w$ on a finite alphabet $A$, the complexity function $p_w$ of $w$ is the sequence counting, for each non-negative $n$, the number $p_w(n)$ of words of length $n$ on the alphabet $A$ that are factors of the infinite…
This paper presents an algorithm for the modification of data compressed using LZ-End, a derivate of LZ77, without prior decompression. The performance of the algorithm and the impact of the modifications on the compression ratio is…
The Sliding Window Lempel-Ziv (SWLZ) algorithm has been studied from various perspectives in information theory literature. In this paper, we provide a general law which defines the asymptotics of match length for stationary and ergodic…
We study the impact that string reversal can have on several repetitiveness measures. First, we exhibit an infinite family of strings where the number, $r$, of runs in the run-length encoding of the Burrows--Wheeler transform (BWT) can…
This paper considers the problem of maintaining statistic aggregates over the last W elements of a data stream. First, the problem of counting the number of 1's in the last W bits of a binary stream is considered. A lower bound of…
The paper introduces a new lossless, highly robust compression algorithm that similar with LZW algorithm, yet the algorithm discards dictionary processing and uses irregular sequences with massive, random information instead. Then the paper…
This paper presents conditional versions of Lempel-Ziv (LZ) algorithm for settings where compressor and decompressor have access to the same side information. We propose a fixed-length-parsing LZ algorithm with side information, motivated…
This paper investigates the size in bits of the LZ77 encoding, which is the most popular and efficient variant of the Lempel-Ziv encodings used in data compression. We prove that, for a wide natural class of variable-length encoders for…
The Burrows-Wheeler Transform (BWT) is an invertible text transformation that permutes symbols of a text according to the lexicographical order of its suffixes. BWT is the main component of popular lossless compression programs (such as…
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…