Related papers: On Network Coding Capacity - Matroidal Networks an…
We investigate the properties of a family of polytopes that naturally arise in connection with a problem in distributed data storage, namely service rate region polytopes. The service rate region of a distributed coded system describes the…
The problem of mismatched decoding for discrete memoryless channels is addressed. A mismatched cognitive multiple-access channel is introduced, and an inner bound on its capacity region is derived using two alternative encoding methods:…
A matroid is supersolvable if it has a maximal chain of flats each of which is modular. A matroid is saturated if every round flat is modular. In this article we present supersolvable saturated matroids as analogues to chordal graphs, and…
We study the achievable capacity regions of full-duplex links in the single- and multi-channel cases (in the latter case, the channels are assumed to be orthogonal -- e.g., OFDM). We present analytical results that characterize the uplink…
We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the…
This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more than z edges. Unlike prior papers, which assume equal capacities on all links, arbitrary link capacities are…
We consider communication over a noisy network under randomized linear network coding. Possible error mechanism include node- or link- failures, Byzantine behavior of nodes, or an over-estimate of the network min-cut. Building on the work…
We investigate the role of cooperation in wireless networks subject to a spatial degrees of freedom limitation. To address the worst case scenario, we consider a free-space line-of-sight type environment with no scattering and no fading. We…
We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…
Scaling model capacity has been vital in the success of deep learning. For a typical network, necessary compute resources and training time grow dramatically with model size. Conditional computation is a promising way to increase the number…
We propose an algebraic geometric framework to study the expressivity of linear activation neural networks. A particular quantity of neural networks that has been actively studied is the number of linear regions, which gives a…
The routing capacity region of networks with multiple unicast sessions can be characterized using Farkas' lemma as an infinite set of linear inequalities. In this paper this result is sharpened by exploiting properties of the solution…
Recent research on distributed storage systems (DSSs) has revealed interesting connections between matroid theory and locally repairable codes (LRCs). The goal of this chapter is to introduce the reader to matroids and polymatroids, and…
For a (single-source) multicast network, the size of a base field is the most known and studied algebraic identity that is involved in characterizing its linear solvability over the base field. In this paper, we design a new class…
The analysis of the modular structure of networks is a major challenge in complex networks theory. The validity of the modular structure obtained is essential to confront the problem of the topology-functionality relationship. Recently,…
The exact calculation of network reliability in a probabilistic context has been a long-standing issue of practical importance, but a difficult one, even for planar graphs, with perfect nodes and with edges of identical reliability p. Many…
This paper presents preliminary results in the definition of a comprehensive benchmark framework designed to systematically evaluate spatial reasoning capabilities in neural networks, with a particular focus on morphological properties such…
In this paper, we explore a connection between binary hierarchical models, their marginal polytopes and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is…
In this paper, we derive the information theoretic capacity of a special class of mesh networks. A mesh network is a heterogeneous wireless network in which the transmission among power limited nodes is assisted by powerful relays, which…
The following \textit{network computing} problem is considered. Source nodes in a directed acyclic network generate independent messages and a single receiver node computes a target function $f$ of the messages. The objective is to maximize…