Related papers: Prefix Codes for Power Laws with Countable Support
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion…
It has been shown in the indexing literature that there is an essential difference between prefix/range searches on the one hand, and predecessor/rank searches on the other hand, in that the former provably allows faster query resolution.…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
We study the compressibility of enumerations in the context of Kolmogorov complexity, focusing on strong and weak forms of compression and their gain: the amount of auxiliary information embedded in the compressed enumeration. The existence…
In the last years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipf's systems, due to the discreteness of the variables and to the existence of two representations…
We investigate the ratio $\rho_{n,L}$ of prefix codes to all uniquely decodable codes over an $n$-letter alphabet and with length distribution $L$. For any integers $n\geq 2$ and $m\geq 1$, we construct a lower bound and an upper bound for…
We investigate the construction of prefix-free and fix-free codes with specified codeword compositions. We present a polynomial time algorithm which constructs a fix-free code with the same codeword compositions as a given code for a…
We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…
Molecular communication (MC) enables information transfer through molecules at the nano-scale. This paper presents new and optimized source coding (data compression) methods for MC. In a recent paper, prefix source coding was introduced…
The capacity achieving probability mass function (PMF) of a finite signal constellation with an average power constraint is in most cases non-uniform. A common approach to generate non-uniform input PMFs is Huffman shaping, which consists…
We describe an extension of Earley's parser for stochastic context-free grammars that computes the following quantities given a stochastic context-free grammar and an input string: a) probabilities of successive prefixes being generated by…
For any finite discrete source, the competitive advantage of prefix code $C_1$ over prefix code $C_2$ is the probability $C_1$ produces a shorter codeword than $C_2$, minus the probability $C_2$ produces a shorter codeword than $C_1$. For…
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…
Language models (LMs) estimate a probability distribution over strings in a natural language; these distributions are crucial for computing perplexity and surprisal in linguistics research. While we are usually concerned with measuring…
We investigate the structural relationship between prefix-free codes over the binary alphabet and a class of unlabeled rooted trees, which we call \emph{symmetric} trees. We establish a canonical correspondence between prefix-free codes and…
Zipf's law in its basic incarnation is an empirical probability distribution governing the frequency of usage of words in a language. As Terence Tao recently remarked, it still lacks a convincing and satisfactory mathematical explanation.…
We introduce a binary embedding framework, called Proximity Preserving Code (PPC), which learns similarity and dissimilarity between data points to create a compact and affinity-preserving binary code. This code can be used to apply fast…
Canonical Huffman code is an optimal prefix-free compression code whose codewords enumerated in the lexicographical order form a list of binary words in non-decreasing lengths. Gagie et al. (2015) gave a representation of this coding…
Probability estimation is an elementary building block of every statistical data compression algorithm. In practice probability estimation is often based on relative letter frequencies which get scaled down, when their sum is too large.…
In this paper, we propose a source coding scheme that represents data from unknown distributions through frequency and support information. Existing encoding schemes often compress data by sacrificing computational efficiency or by assuming…