Related papers: A Fully Pipelined FIFO Based Polynomial Multiplica…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
Cryptanalysis of block ciphers involves massive computations which are independent of each other and can be instantiated simultaneously so that the solution space is explored at a faster rate. With the advent of low cost Field Programmable…
The precise analysis and accurate measurement of harmonic provides a reliable scientific industrial application. However, the high-performance DSP processor is the important method of electrical harmonic analysis. Hence, in this research…
This paper presents a low-latency hardware accelerator for modular polynomial multiplication for lattice-based post-quantum cryptography and homomorphic encryption applications. The proposed novel modular polynomial multiplier exploits the…
In this work, we explore an energy-efficient implementation of the polyphase network for a filter bank multicarrier (FBMC) system. The network is approximated using a greedy algorithm based on matching pursuits (MP) that converts the…
We recently introduced the Fast Newton Transform (FNT), an hierarchical algorithm for performing multivariate Newton interpolation in arbitrary downward closed polynomial spaces of spatial dimension $m$. Here, we analyze the FNT in the…
An alternative to the matrix inverse procedure is presented. Given a bit register which is arbitrarily large, the matrix inverse to an arbitrarily large matrix can be peformed in ${\cal O}(N^2)$ operations, and to matrix multiplication on a…
This paper presents the first parallel implementation of the novel "Interpolated Factored Green Function" (IFGF) method introduced recently for the accelerated evaluation of discrete integral operators arising in wave scattering and other…
The truncated Fourier transform (TFT) was introduced by van der Hoeven in 2004 as a means of smoothing the "jumps" in running time of the ordinary FFT algorithm that occur at power-of-two input sizes. However, the TFT still introduces these…
Decimal multiplication is the task of multiplying two numbers in base $10^N.$ Specifically, we focus on the number-theoretic transform (NTT) family of algorithms. Using only portable techniques, we achieve a 3x-5x speedup over the mpdecimal…
We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the…
Transformer-based large language models (LLMs) rely heavily on intensive matrix multiplications for attention and feed-forward layers, with the Q, K, and V linear projections in the Multi-Head Self-Attention (MHA) module constituting a…
This paper presents a comprehensive exploration of Fast Fourier Transform (FFT) and linear convolution implementations, integrating both conventional methods and novel approaches leveraging the Bit Slicing Multiplier (BSM) technique. The…
In the multi-cell multiuser multi-input multi-output (MU-MIMO) systems, fractional programming (FP) has demonstrated considerable effectiveness in optimizing beamforming vectors, yet it suffers from high computational complexity. Recent…
Fast time-domain algorithms have been developed in signal processing applications to reduce the multiplication complexity. For example, fast convolution structures using Cook-Toom and Winograd algorithms are well understood. Short length…
In this paper, the authors propose the idea of a combined integer and floating point multiplier(CIFM) for FPGAs. The authors propose the replacement of existing 18x18 dedicated multipliers in FPGAs with dedicated 24x24 multipliers designed…
Galois field (GF) arithmetic circuits find numerous applications in communications, signal processing, and security engineering. Formal verification techniques of GF circuits are scarce and limited to circuits with known bit positions of…
Matrix multiplication is a cornerstone operation in a wide array of scientific fields, including machine learning and computer graphics. The standard algorithm for matrix multiplication has a complexity of $\mathcal{O}(n^3)$ for $n\times n$…
General-purpose multiprocessors (as, in our case, Intel IvyBridge and Intel Haswell) increasingly add GPU computing power to the former multicore architectures. When used for embedded applications (for us, Synthetic aperture radar) with…
We discuss a simple, binary tree-based algorithm for the collective allreduce (reduction-to-all, MPI_Allreduce) operation for parallel systems consisting of $p$ suitably interconnected processors. The algorithm can be doubly pipelined to…