Related papers: Vector Network Coding Based on Subspace Codes Outp…
Compressing large neural networks is an important step for their deployment in resource-constrained computational platforms. In this context, vector quantization is an appealing framework that expresses multiple parameters using a single…
We consider the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a proper subset of the network edges. We model this problem via an adversarial noise, presenting a formal…
Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of $\F_q^n$ with a given dimension. A computer search for large constant…
We consider the delay of network coding compared to routing with retransmissions in packet erasure networks with probabilistic erasures. We investigate the sub-linear term in the block delay required for unicasting $n$ packets and show that…
Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the…
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…
Vector perturbation is an encoding method for broadcast channels in which the transmitter solves a shortest vector problem in a lattice to create a perturbation vector, which is then added to the data before transmission. In this work, we…
This dissertation considers new constructions and decoding approaches for error-correcting codes based on non-conventional polynomials, with the objective of providing new coding solutions to the applications mentioned above. With skew…
The \emph{index coding} problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad-hoc networks. An instance of the index coding problem includes a…
The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over…
Increasing network utilization is often considered as the holy grail of communications. In this article, the concept of sub-rate coding and decoding in the framework of linear network coding (LNC) is discussed for single-source…
Random Linear Network Coding (RLNC) is a transmission scheme that opts for linear combinations of the transmitted packets at a subset of the intermediate nodes. This scheme is usually considered when Network Coding (NC) is desired over…
We develop a network coding technique based on flags of subspaces and a corresponding network channel model. To define error correcting codes we introduce a new distance on the flag variety, the Grassmann distance on flags and compare it to…
Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required…
We show that the network coding and index coding problems are equivalent. This equivalence holds in the general setting which includes linear and non-linear codes. Specifically, we present an efficient reduction that maps a network coding…
Network coding (NC), in principle, is a Layer-3 innovation that improves network throughput in wired networks for multicast/broadcast scenarios. Due to the fundamental differences between wired and wireless networks, extending NC to…
We consider the problem of serving multicast flows in a crossbar switch. We show that linear network coding across packets of a flow can sustain traffic patterns that cannot be served if network coding were not allowed. Thus, network coding…
Subspace codes and rank-metric codes can be used to correct errors and erasures in network, with linear network coding. Subspace codes were introduced by Koetter and Kschischang to correct errors and erasures in networks where topology is…
We study network coding gaps for the problem of makespan minimization of multiple unicasts. In this problem distinct packets at different nodes in a network need to be delivered to a destination specific to each packet, as fast as possible.…
Secure network coding realizes the secrecy of the message when the message is transmitted via noiseless network and a part of edges or a part of intermediate nodes are eavesdropped. In this framework, if the channels of the network has…