Related papers: Galois Field Arithmetics for Linear Network Coding…
When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…
In this paper, we develop an efficient decoder via the proximal alternating direction method of multipliers (proximal-ADMM) technique for nonbinary linear block codes in the Galois field. Its main contents are as follows: first, exploiting…
Linear algebra operations have been widely used in big data analytics and scientific computations. Many works have been done on optimizing linear algebra operations on GPUs with regular-shaped input. However, few works focus on fully…
This work provides a comprehensive derivation of the parameter gradients for GATv2 [4], a widely used implementation of Graph Attention Networks (GATs). GATs have proven to be powerful frameworks for processing graph-structured data and,…
One of the oldest problems in coding theory is to match the Gilbert-Varshamov bound with explicit binary codes. Over larger-yet still constant-sized-fields, algebraic-geometry codes are known to beat the GV bound. In this work, we leverage…
We present a new general method for performing basic arithmetic in the finite field~$\mathbb{F}_p$ for any prime $p>2$ by using traditional binary operations over~$\mathbb{F}_2$. Our new approach is efficient and competitive with current…
Extremely large-scale multiple-input-multiple-output (XL-MIMO) is a promising technique to achieve ultra-high spectral efficiency for future 6G communications. The mixed line-of-sight (LoS) and non-line-of-sight (NLoS) XL-MIMO near-field…
Recent years have seen substantial progress in neural generation of text, images, and audio, supported by mature training pipelines and large-scale optimization. For graphs, however, comparable progress has been more limited. We attribute…
In this letter, we evaluate the finite-length performance of network coding when using either random or structured encoding matrices. First, we present our novel construction of structured network codes over Fq (q = 2^m) using Pascal…
This paper considers vector network coding based on rank-metric codes and subspace codes. Our main result is that vector network coding can significantly reduce the required field size compared to scalar linear network coding in the same…
We construct optimal secure coded distributed schemes that extend the known optimal constructions over fields of characteristic 0 to all fields. A serendipitous result is that we can encode \emph{all} functions over finite fields with a…
Extremely large-scale MIMO (XL-MIMO) is a promising technique for future 6G communications. The sharp increase in the number of antennas causes electromagnetic propagation to change from far-field to near-field. Due to the near-field…
An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding…
Satellite networks provide unique challenges that can restrict users' quality of service. For example, high packet erasure rates and large latencies can cause significant disruptions to applications such as video streaming or voice-over-IP.…
Bayesian methodologies prioritising accurate associations above sparsity in Gaussian graphical model (GGM) estimation remain relatively scarce in scientific literature. It is well accepted that the $\ell_2$ penalty enjoys a smaller…
For analysing real-world networks, graph representation learning is a popular tool. These methods, such as a graph autoencoder (GAE), typically rely on low-dimensional representations, also called embeddings, which are obtained through…
This paper presents the first decoding algorithm for Gabidulin codes over Galois rings with provable quadratic complexity. The new method consists of two steps: (1) solving a syndrome-based key equation to obtain the annihilator polynomial…
Software is often used for Network Functions (NFs) -- such as firewalls, NAT, deep packet inspection, and encryption -- that are applied to traffic in the network. The community has hoped that NFV would enable rapid development of new NFs…
In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including…
We initiate the study of what we term ``fast good codes'' with ``fast good duals.'' Specifically, we consider the task of constructing a rate 1/2 binary linear code such that both it and its dual are asymptotically good (in fact, have…