Related papers: Galois Field Arithmetics for Linear Network Coding…
Graph algorithms are at the heart of several applications, and achieving high performance with them has become critical due to the tremendous growth of irregular data. However, irregular algorithms are quite challenging to parallelize…
SSE (streaming SIMD extensions) and AVX (advanced vector extensions) are SIMD (single instruction multiple data streams) instruction sets supported by recent CPUs manufactured in Intel and AMD. This SIMD programming allows parallel…
Cyclotomic fast Fourier transforms (CFFTs) are efficient implementations of discrete Fourier transforms over finite fields, which have widespread applications in cryptography and error control codes. They are of great interest because of…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
Finite field multiplier is mainly used in error-correcting codes and signal processing. Finite field multiplier is regarded as the bottleneck arithmetic unit for such applications and it is the most complicated operation over finite field…
In this paper, we investigate the optimal precoding scheme for relay networks with finite-alphabet constraints. We show that the previous work utilizing various design criteria to maximize either the diversity order or the transmission rate…
Greaves et al. (2022) extended frames over real or complex numbers to frames over finite fields. In this paper, we study the theory of frames over finite fields by incorporating the Galois inner products introduced by Fan and Zhang (2017),…
Graph Augmentation Learning (GAL) provides outstanding solutions for graph learning in handling incomplete data, noise data, etc. Numerous GAL methods have been proposed for graph-based applications such as social network analysis and…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
In recent years, network coding has emerged as an innovative method that helps wireless network approaches its maximum capacity, by combining multiple unicasts in one broadcast. However, the majority of research conducted in this area is…
In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a…
Graph Convolutional Networks (GCNs) have emerged as the state-of-the-art graph learning model. However, it can be notoriously challenging to inference GCNs over large graph datasets, limiting their application to large real-world graphs and…
Network Function Virtualization (NFV) prescribes the instantiation of network functions on general-purpose network devices, such as servers and switches. While yielding a more flexible and cost-effective network architecture, NFV is…
This note presents Galois theory for finite fields. It was written as a handout for the MAT401 course ``Polynomial equations and fields'' taught at the University of Toronto in Spring 2026. We use without proofs some basic properties of…
Link Prediction (LP) is a crucial problem in graph-structured data. Graph Neural Networks (GNNs) have gained prominence in LP, with Graph AutoEncoders (GAEs) being a notable representation. However, our empirical findings reveal that GAEs'…
This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…
One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…
In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary…
Bridge++ is a general-purpose code set for a numerical simulation of lattice QCD aiming at a readable, extensible, and portable code while keeping practically high performance. The previous version of Bridge++ is implemented in double…