Related papers: A Characterization of Optimal Prefix Codes
We consider a distributed source coding system in which several observations are communicated to the decoder using limited transmission rate. The observations must be separately coded. We introduce a robust distributed coding scheme which…
In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding simultaneously. The existence of…
We give results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous weight. This article improves on the existing Plotkin bound derived in an earlier paper, and suggests a version of a…
We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties of the sequence of finite words obtained by coding a typical…
We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices.…
A multifold $1$-perfect code ($1$-perfect code for list decoding) in any graph is a set $C$ of vertices such that every vertex of the graph is at distance not more than $1$ from exactly $\mu$ elements of $C$. In $q$-ary Hamming graphs,…
Strong alt-induced codes, a particular case of alt-induced codes, has been introduced and considered by D. L. Van and the author in earlier papers. In this note, an algorithm to check whether a regular code is strong alt-induced or not is…
We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p$ over a poset is monotone if, for any pair of domain elements $x$ and $y$ such that $x \preceq y$,…
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…
A method for finding an optimum $n$-dimensional commutative group code of a given order $M$ is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of…
Originally introduced and studied by the third and fourth authors together with J. Justin and S. Widmer in arXiv:0801.1656, rich words constitute a new class of finite and infinite words characterized by containing the maximal number of…
Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…
We consider the problem of sequencing a set of positive numbers. We try to find the optimal sequence to maximize the variance of its partial sums. The optimal sequence is shown to have a beautiful structure. It is interesting to note that…
A long standing problem in the area of error correcting codes asks whether there exist good cyclic codes. Most of the known results point in the direction of a negative answer. The uncertainty principle is a classical result of harmonic…
We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length…
The set of finite words over a well-quasi-ordered set is itself well-quasi-ordered. This seminal result by Higman is a cornerstone of the theory of well-quasi-orderings and has found numerous applications in computer science. However, this…
Recently, prefix-tuning has gained increasing attention as a parameter-efficient finetuning method for large-scale pretrained language models. The method keeps the pretrained models fixed and only updates the prefix token parameters for…
A prefix code L satisfies the condition that no word of L is a proper prefix of another word of L. Recently, Ko, Han and Salomaa relaxed this condition by allowing a word of L to be a proper prefix of at most k words of L, for some `margin'…