Related papers: Unicast-Uniprior Index Coding Problems: Minrank an…
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…
We study the leader election problem in oriented ring networks under content-oblivious asynchronous message-passing systems, where an adversary may arbitrarily corrupt message contents. Frei et al. (DISC 2024) presented a uniform…
We prove a generalization to Jennrich's uniqueness theorem for tensor decompositions in the undercomplete setting. Our uniqueness theorem is based on an alternative definition of the standard tensor decomposition, which we call…
The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn…
The minrank of a graph $G$ is the minimum rank of a matrix $M$ that can be obtained from the adjacency matrix of $G$ by switching some ones to zeros (i.e., deleting edges) and then setting all diagonal entries to one. This quantity is…
Prevalent lossy image compression schemes can be divided into: 1) explicit image compression (EIC), including traditional standards and neural end-to-end algorithms; 2) implicit image compression (IIC) based on implicit neural…
The problem of securing a network coding communication system against an eavesdropper adversary is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the adversary can eavesdrop…
It is known that there exists a multiple-unicast network which has a rate $1$ linear network coding solution if and only if the characteristic of the finite field belongs to a given finite or co-finite set of primes. In this paper, we show…
This paper deals with vector linear index codes for multiple unicast index coding problems where there is a source with K messages and there are K receivers each wanting a unique message and having symmetric (with respect to the receiver…
We consider a wireless broadcast station that transmits packets to multiple users. The packet requests for each user may overlap, and some users may already have certain packets. This presents a problem of broadcasting in the presence of…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
Index coding, or broadcasting with side information, is a network coding problem of most fundamental importance. In this problem, given a directed graph, each vertex represents a user with a need of information, and the neighborhood of each…
The index coding problem is a fundamental transmission problem which occurs in a wide range of multicast networks. Network coding over a large finite field size has been shown to be a theoretically efficient solution to the index coding…
Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…
PAR-constrained sequences are widely used in communication systems and radars due to various practical needs; specifically, sequences are required to be unimodular or of low peak-to-average power ratio (PAR). For unimodular sequence design,…
Partial clique covering is one of the most basic coding schemes for index coding problems, generalizing clique and cycle covering on the side information digraph and further reducing the achievable broadcast rate. In this paper, we start…
We introduce the blind index coding (BIC) problem, in which a single sender communicates distinct messages to multiple users over a shared channel. Each user has partial knowledge of each message as side information. However, unlike classic…
A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding,…
An interference alignment perspective is used to identify the simplest instances (minimum possible number of edges in the alignment graph, no more than 2 interfering messages at any destination) of index coding problems where non-Shannon…