Related papers: Equidistant Linear Network Codes with maximal Erro…
In this paper, we study the data gathering problem in the context of power grids by using a network of sensors, where the sensed data have inter-node redundancy. Specifically, we propose a new transmission method, calledquantized network…
Network embedding is a highly effective method to learn low-dimensional node vector representations with original network structures being well preserved. However, existing network embedding algorithms are mostly developed for a single…
The problem of securing a network coding communication system against a wiretapper adversary is considered. The network implements linear network coding to deliver $n$ packets from source to each receiver, and the wiretapper can eavesdrop…
Consider the asymmetric broadcast channel with a random superposition codebook, which may be comprised of constant composition or \iid codewords. By applying Forney's optimal decoder for individual messages and the message pair for the…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph…
Practical random network coding based schemes for multicast include a header in each packet that records the transformation between the sources and the terminal. The header introduces an overhead that can be significant in certain…
Network embedding represents nodes in a continuous vector space and preserves structure information from the Network. Existing methods usually adopt a "one-size-fits-all" approach when concerning multi-scale structure information, such as…
In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices $W_{t,n,k}$, representing $t$-element subsets versus $k$-element subsets of an $n$-element set. We provide…
In this paper, we introduce code distances, a new family of invariants for linear codes. We establish some properties and prove bounds on the code distances, and show that they are not invariants of the matroid (for a linear block code) or…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such…
Conventional communication systems are mainly designed to reduce error rates and increase transmission rates, and therefore usually provide uniform protection to all transmitted messages. However, in intent-oriented applications, different…
The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over…
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…
It is known a vector linear solution may exist if and only if the characteristic of the finite field belongs to a certain set of primes. But, can increasing the message dimension make a network vector linearly solvable over a larger set of…
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…
We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques. An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly…