Related papers: How to Compute Modulo Prime-Power Sums
A new class of structured codes called Quasi Group Codes (QGC) is introduced. A QGC is a subset of a group code. In contrast with group codes, QGCs are not closed under group addition. The parameters of the QGC can be chosen such that the…
The problem of reliable communication over the multiple-access channel (MAC) with states is investigated. We propose a new coding scheme for this problem which uses quasi-group codes (QGC). We derive a new computable single-letter…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
The problem of computing sum of sources over a multiple access channel (MAC) is considered. Building on the technique of linear computation coding (LCC) proposed by Nazer and Gastpar [2007], we employ the ensemble of nested coset codes to…
We obtain explicit estimates for the mixed character sum $S= S(\chi,g,f,p^m) = \sum_{x=1}^{p^m} \chi (g(x)) e_{p^m}(f(x))$, where $p^m$ is a prime power, $\chi$ is a multiplicative character mod $p^m$ and $f,g$ are rational functions over…
Polar codes are the first error-correcting codes to provably achieve the channel capacity but with infinite codelengths. For finite codelengths the existing decoder architectures are limited in working frequency by the partial sums…
Multi-party computation (MPC) is promising for designing privacy-preserving machine learning algorithms at edge networks. An emerging approach is coded-MPC (CMPC), which advocates the use of coded computation to improve the performance of…
Following the approach by R. K\"otter and F. R. Kschischang, we study network codes as families of k-dimensional linear subspaces of a vector space F_q^n, q being a prime power and F_q the finite field with q elements. In particular,…
In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…
In this paper, we present a novel variation of the coded matrix multiplication problem which we refer to as fully private grouped matrix multiplication (FPGMM). In FPGMM, a master wants to compute a group of matrix products between two…
In this paper, two new families of MDS quantum convolutional codes are constructed. The first one can be regarded as a generalization of \cite[Theorem 6.5]{GGGlinear}, in the sense that we do not assume that $q\equiv1\pmod{4}$. More…
As society becomes more reliant on computers, cryptographic security becomes increasingly important. Current encryption schemes include the ElGamal signature scheme, which depends on the complexity of the discrete logarithm problem. It is…
This article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers. Algorithms are described that compute the maximum integer modulo which two monic coprime integral polynomials…
We investigate the problem of privacy preserving distributed matrix multiplication in edge networks using multi-party computation (MPC). Coded multi-party computation (CMPC) is an emerging approach to reduce the required number of workers…
We consider the problem of finding optimal, fair and distributed power-rate strategies to achieve the sum capacity of the Gaussian multiple-access block-fading channel. In here, the transmitters have access to only their own fading…
In this paper, due to the important value in practical applications, we consider the coded distributed matrix multiplication problem of computing $AA^\top$ in a distributed computing system with $N$ worker nodes and a master node, where the…
We study computation of a modulo-sum of two binary source sequences over a two-user erasure multiple access channel. The channel is modeled as a binary-input, erasure multiple access channel, which can be in one of three states - either the…
We consider the task of communicating a generic bivariate function of two classical sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at…
In this article we compute the $q$th power values of the quadratic polynomials $f$ with negative squarefree discriminant such that $q$ is coprime to the class number of the splitting field of $f$ over $\mathbb{Q}$. The theory of unique…