Related papers: On Network Coding Capacity - Matroidal Networks an…
A combinatorial framework for adversarial network coding is presented. Channels are described by specifying the possible actions that one or more (possibly coordinated) adversaries may take. Upper bounds on three notions of capacity (the…
Characterizing the capacity region of multi-source wireless relay networks is one of the fundamental issues in network information theory. The problem is, however, quite challenging due to inter-user interference when there exist multiple…
In this paper, we use entropy functions to characterise the set of rate-capacity tuples achievable with either zero decoding error, or vanishing decoding error, for general network coding problems. We show that when sources are colocated,…
We investigate the service-rate region (SRR) of distributed storage systems that employ linear codes. We focus on systems where each server stores one code symbol, and a user recovers a data symbol by accessing any of its recovery groups,…
In this study, we consider a class of linear matroid interdiction problems, where the feasible sets for the upper-level decision-maker (referred to as a leader) and the lower-level decision-maker (referred to as a follower) are induced by…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
In coding theory, a common question is to understand the threshold rates of various local properties of codes, such as their list decodability and list recoverability. A recent work Levi, Mosheiff, and Shagrithaya (FOCS 2025) gave a novel…
This paper follows very closely a famous paper by Csisz\'{a}r and K\"{o}rner about classical (non-quantum) wiretap coding. Our paper gives a self-contained and slightly novel review of some important results of the paper by Csisz\'{a}r and…
Fixed-size commutative rings are quasi-ordered such that all scalar linearly solvable networks over any given ring are also scalar linearly solvable over any higher-ordered ring. As consequences, if a network has a scalar linear solution…
This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to operate only on a prescribed subset of edges, classical cut-set…
We consider the problem of computing the capacity of a coded, multicast network over a small alphabet. We introduce a novel approach to this problem based on mixed integer programming. As an application of our approach, we recover, extend…
Motivated by communication through a network employing linear network coding, capacities of linear operator channels (LOCs) with arbitrarily distributed transfer matrices over finite fields are studied. Both the Shannon capacity $C$ and the…
In this paper we consider the problem of secure network coding where an adversary has access to an unknown subset of links chosen from a known collection of links subsets. We study the capacity region of such networks, commonly called…
In this paper we consider the identification (ID) via multiple access channels (MACs). In the general MAC the ID capacity region includes the ordinary transmission (TR) capacity region. In this paper we discuss the converse coding theorem.…
We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A special case of this correspondence identifies the problem of…
In this paper, a link between polymatroid theory and locally repairable codes (LRCs) is established. The codes considered here are completely general in that they are subsets of $A^n$, where $A$ is an arbitrary finite set. Three classes of…
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…
The encoding complexity of network coding for single multicast networks has been intensively studied from several aspects: e.g., the time complexity, the required number of encoding links, and the required field size for a linear code…
Network coding theory studies the transmission of information in networks whose vertices may perform nontrivial encoding and decoding operations on data as it passes through the network. The main approach to deciding the feasibility of…
Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1)…