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We consider a setup in which Alice selects a pdf $f$ from a set of prescribed pdfs $\mathscr{P}$ and sends a prefix-free codeword $W$ to Bob in order to allow him to generate a single instance of the random variable $X\sim f$. We describe a…
In this paper we provide a method to obtain tight lower bounds on the minimum redundancy achievable by a Huffman code when the probability distribution underlying an alphabet is only partially known. In particular, we address the case where…
Separable Non-negative Matrix Factorization (SNMF) is an important method for topic modeling, where "separable" assumes every topic contains at least one anchor word, defined as a word that has non-zero probability only on that topic. SNMF…
A new scheme for the problem of centralized coded caching with non-uniform demands is proposed. The distinguishing feature of the proposed placement strategy is that it admits equal sub-packetization for all files while allowing the users…
We consider the canonical {\em shared link network} formed by a source node, hosting a library of $m$ information messages (files), connected via a noiseless common link to $n$ destination nodes (users), each with a cache of size M files.…
Pre-transformed polar codes (PTPCs) form a class of codes that perform close to the finite-length capacity bounds. The minimum distance and the number of minimum weight codewords are two decisive properties for their performance. In this…
Bounds on linear codes play a central role in coding theory, as they capture the fundamental trade-off between error-correction capability (minimum distance) and information rate (dimension relative to length). Classical results…
A constant weight binary code consists of $n$-bit binary codewords, each with exactly $w$ bits equal to 1, such that any two codewords are at least Hamming distance $d$ apart. $A(n,d,w)$ is the maximum size of a constant weight binary code…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
This paper addresses the problem of identifying palindromic factors in texts that include wildcards -- special characters that match all others. These symbols challenge many classical algorithms, as numerous combinatorial properties are not…
The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to…
Consider a channel with a given input alphabet size and a given input distribution. Our aim is to degrade or upgrade it to a channel with at most L output letters. The paper contains four main results. The first result, from which the paper…
We revisit the source coding problem for a Markov chain under the assumption that the transmission times and how fast the Markov chain transitions its state happen at the same time-scale. Specifically, we assume that the transmission of…
Code completion is widely used by software developers to provide coding suggestions given a partially written code snippet. Apart from the traditional code completion methods, which only support single token completion at minimal positions,…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
This paper presents an $O(\log\log \bar{d})$ round massively parallel algorithm for $1+\epsilon$ approximation of maximum weighted $b$-matchings, using near-linear memory per machine. Here $\bar{d}$ denotes the average degree in the graph…
In order to understand the performance of a code under maximum-likelihood (ML) decoding, it is crucial to know the minimal codewords. In the context of linear programming (LP) decoding, it turns out to be necessary to know the minimal…
A rateless code encodes a finite length information word into an infinitely long codeword such that longer prefixes of the codeword can tolerate a larger fraction of errors. A rateless code achieves capacity for a family of channels if, for…
Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…
This paper describes a new set of block source codes well suited for data compression. These codes are defined by sets of productions rules of the form a.l->b, where a in A represents a value from the source alphabet A and l, b are -small-…