Related papers: Reviewed of the compression limit of an individual…
Given the importance of the claim, we want to start by exposing the following consideration: this claim comes out more than a year after the article "Practical applications of Set Shaping Theory in Huffman coding" which reports the program…
Set Shaping Theory (SST) moves beyond the classical fixed-space model by constructing bijective mappings the original sequence set into structured regions of a larger sequence space. These shaped subsets are characterized by a reduced…
In the paper, a theoretical work is done for investigating effects of splitting data sequence into packs of data set. We proved that a partitioning of data sequence is possible to find such that the entropy rate at each subsequence is lower…
We extend Ziv and Lempel's model of finite-state encoders to the realm of lossy compression of individual sequences. In particular, the model of the encoder includes a finite-state reconstruction codebook followed by an information lossless…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
This paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in…
It is shown that an i.i.d. binary source sequence $X_1, \ldots, X_n$ can be losslessly compressed at any rate above entropy such that the individual decoding of any $X_i$ reveals \emph{no} information about the other bits $\{X_j : j \neq…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
To render a sequence testable, namely capable of identifying and detecting errors, it is necessary to apply a transformation that increases its length by introducing statistical dependence among symbols, as commonly exemplified by the…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
This paper explores an innovative aspect of the Set Shaping Theory, the use of a negative shaping order K. Traditionally, the theory utilizes a positive K to extend the length of data strings, enhancing their testability and…
This article describes lossless compression algorithms for multisets of sequences, taking advantage of the multiset's unordered structure. Multisets are a generalisation of sets where members are allowed to occur multiple times. A multiset…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
In this article, we define the Set Shaping Theory whose goal is the study of the bijection functions that transform a set of strings into a set of equal size made up of strings of greater length. The functions that meet this condition are…
In developing locally testable codes, information is added to the coded message by creating redundancy in the codewords. In this article, we propose an alternative method in which redundancy is introduced on the message that must be…
Large alphabet source coding is a basic and well-studied problem in data compression. It has many applications such as compression of natural language text, speech and images. The classic perception of most commonly used methods is that a…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
Motivated by the problem of the definition of a distance between two sequences of characters, we investigate the so-called learning process of typical sequential data compression schemes. We focus on the problem of how a compression…
The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…