Related papers: Combinatorial Entropy Encoding
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…
In this paper will be presented new approach to entropy coding: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetric numeral systems - optimal for freely…
Data compression has become a necessity not only the in the field of communication but also in various scientific experiments. The data that is being received is more and the processing time required has also become more. A significant…
We study the following one-way asymmetric transmission problem, also a variant of model-based compressed sensing: a resource-limited encoder has to report a small set $S$ from a universe of $N$ items to a more powerful decoder (server). The…
Hypergraphs provide a natural representation for many-to-many relationships in data-intensive applications, yet their scalability is often hindered by high memory consumption. While prior work has improved computational efficiency, reducing…
In this paper, source coding or data compression is viewed as a measurement problem. Given a measurement device with fewer states than the observable of a stochastic source, how can one capture the essential information? We propose modeling…
This paper proposes a novel model of the two-level scalar quantizer with extended Huffman coding. It is designed for the average bit rate to approach the source entropy as close as possible provided that the signal to quantization noise…
Grammar compression represents a string as a context free grammar. Achieving compression requires encoding such grammar as a binary string; there are a few commonly used encodings. We bound the size of practically used encodings for several…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The algorithm uses a weighted average of the Shannon Entropies of the string and all but the last binary…
Compression algorithms reduce the redundancy in data representation to decrease the storage required for that data. Data compression offers an attractive approach to reducing communication costs by using available bandwidth effectively.…
Machine learning has had a major impact on data compression over the last decade and inspired many new, exciting theoretical and applied questions. This paper describes one such direction -- relative entropy coding -- which focuses on…
The context transformation and generalized context transformation methods, we introduced recently, were able to reduce zero order entropy by exchanging digrams, and as a consequence, they were removing mutual information between consecutive…
A prescription to calculate the minimum number of bits needed for binary strip detector readout is presented. This permits a systematic analysis of the readout efficiency relative to this theoretical minimum number of bits. Different level…
Assessing whether two datasets are distributionally consistent is central to modern scientific analysis, particularly as generative artificial intelligence produces synthetic data whose fidelity must be validated against real observations…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
We propose a framework for joint entropy coding and encryption using Chaotic maps. We begin by observing that the message symbols can be treated as the symbolic sequence of a discrete dynamical system. For an appropriate choice of the…
The paper presents a binarization scheme that converts non-binary data into a set of binary strings. At present, there are many binarization algorithms, but they are optimal for only specific probability distributions of the data source.…
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…
Entropy quantifies the number of bits required to store objects under certain given assumptions. While this is a well established concept for strings, in the context of tries the state-of-the-art regarding entropies is less developed. The…