Related papers: Galois Field Arithmetics for Linear Network Coding…
This paper proposes CodeX, an end-to-end framework that facilitates encoding, bitwidth customization, fine-tuning, and implementation of neural networks on FPGA platforms. CodeX incorporates nonlinear encoding to the computation flow of…
One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates…
A fundamental problem in coding theory is the design of an efficient coding scheme that achieves the capacity of the additive white Gaussian (AWGN) channel. The main objective of this short note is to point out that by concatenating a…
Graph Neural Networks (GNNs) have made significant advances on several fundamental inference tasks. As a result, there is a surge of interest in using these models for making potentially important decisions in high-regret applications.…
We propose two application-layer coding schemes for delay-constrained point-to-point packet communications with restrictions on the transmitter's maximum duty-cycle. The schemes operate over GF(2) and utilize intermittently available…
Fast encoding and decoding of codes have been always an important topic in code theory as well as complexity theory. Although encoding is easier than decoding in general, designing an encoding algorithm of codes of length $N$ with…
Web developers use base64 formats to include images, fonts, sounds and other resources directly inside HTML, JavaScript, JSON and XML files. We estimate that billions of base64 messages are decoded every day. We are motivated to improve the…
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Yet despite their efficiency, computations remain expensive…
Low-Rank Parity-Check (LRPC) codes are a class of rank metric codes that have many applications specifically in network coding and cryptography. Recently, LRPC codes have been extended to Galois rings which are a specific case of finite…
Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. Some of its practical drawbacks are the complexity of decoding and the overhead due to the coding vectors. For computationally weak and battery-driven…
This study evaluates AoS-to-SoA transformations over reduced-precision data layouts for a particle simulation code on several GPU platforms: We hypothesize that SoA fits particularly well to SIMT, while AoS is the preferred storage format…
This paper introduces new constructions of sum-rank metric codes derived from algebraic function fields, as existing results on such codes remain limited. A major challenge lies in the determination of their parameters. We address this…
We present theoretical and practical results on the order theory of lattices of functions, focusing on Galois connections that abstract (sets of) functions - a topic known as higher-order abstract interpretation. We are motivated by the…
We study space-pass tradeoffs in graph streaming algorithms for parameter estimation and property testing problems such as estimating the size of maximum matchings and maximum cuts, weight of minimum spanning trees, or testing if a graph is…
This is a book about computational aspects of modular forms and the Galois representations attached to them. The main result is the following: Galois representations over finite fields attached to modular forms of level one can, in almost…
Large Language Models (LLMs) have demonstrated strong reasoning abilities, making them suitable for complex tasks such as graph computation. Traditional reasoning steps paradigm for graph problems is hindered by unverifiable steps, limited…
The error coefficient of a linear code is defined as the number of minimum-weight codewords. In an additive white Gaussian noise channel, optimal linear codes with the smallest error coefficients achieve the best possible asymptotic frame…
We study the arithmetic of division fields of semistable abelian varieties A over the rationals. The Galois group of the 2-division field of A is analyzed when the conductor is odd and squarefree. The irreducible semistable mod 2…
We examine the issue of separation and code design for networks that operate over finite fields. We demonstrate that source-channel (or source-network) separation holds for several canonical network examples like the noisy multiple access…
Using an algebraic approach based on the theory of Coxeter groups, we design, and describe the performance of, a class of line codes for parallel transmission of $b$ bits over $b+1$ wires that admit especially simple encoding and decoding…