Related papers: Optimal alphabet for single text compression
The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding -- under an arbitrary coding scheme -- and show that it predicts Zipf's…
There is a large literature devoted to the problem of finding an optimal (min-cost) prefix-free code with an unequal letter-cost encoding alphabet of size. While there is no known polynomial time algorithm for solving it optimally there are…
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…
Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many…
We give the first algorithm for adaptive alphabetic prefix-free coding that is worst-case optimal in terms of time and compression when $\sigma \in o \left( \frac{n^{1 / 2}}{\log n} \right)$, where $\sigma$ is the size of the alphabet and…
Most of the attention in statistical compression is given to the space used by the compressed sequence, a problem completely solved with optimal prefix codes. However, in many applications, the storage space used to represent the prefix…
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…
This article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords.…
This paper proposes a novel entropy encoding technique for lossless data compression. Representing a message string by its lexicographic index in the permutations of its symbols results in a compressed version matching Shannon entropy of…
Text compression schemes and compact data structures usually combine sophisticated probability models with basic coding methods whose average codeword length closely match the entropy of known distributions. In the frequent case where basic…
There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range…
Semantic communication stands out as a highly promising avenue for future developments in communications. Theoretically, source compression coding based on semantics can achieve lower rates than Shannon entropy. This paper introduces a…
Huffman Compression, also known as Huffman Coding, is one of many compression techniques in use today. The two important features of Huffman coding are instantaneousness that is the codes can be interpreted as soon as they are received and…
A new method for constructing minimum-redundancy binary prefix codes is described. Our method does not explicitly build a Huffman tree; instead it uses a property of optimal prefix codes to compute the codeword lengths corresponding to the…
The short message service (SMS) is a wireless medium of transmission that allows you to send brief text messages. Cell phone devices have an uttermost SMS capacity of 1,120 bits in the traditional system. Moreover, the conventional SMS…
The compression is an important topic in computer science which allows we to storage more amount of data on our data storage. There are several techniques to compress any file. In this manuscript will be described the most important…
A finite deterministic (semi)automaton $\mathcal{A} =(Q,\Sigma,\delta)$ is $k$-compressible if there is some word $w\in \Sigma^+$ such that the image of its state set $Q$ under the natural action of $w$ is reduced by at least $k$ states.…
Training and serving Large Language Models (LLMs) relies heavily on parallelization and collective operations, which are frequently bottlenecked by network bandwidth. Lossless compression using e.g., Huffman codes can alleviate the issue,…
We propose a method to improve traditional character-based PPM text compression algorithms. Consider a text file as a sequence of alternating words and non-words, the basic idea of our algorithm is to encode non-words and prefixes of words…
Zipf's law of abbreviation, namely the tendency of more frequent words to be shorter, has been viewed as a manifestation of compression, i.e. the minimization of the length of forms -- a universal principle of natural communication.…