Related papers: Construction of dyadic MDS matrices for cryptograp…
This paper describes a non-homogeneous distributed storage systems (DSS), where there is one super node which has a larger storage size and higher reliability and availability than the other storage nodes. We propose three distributed…
Coded distributed matrix multiplication (CDMM) schemes, such as MatDot codes, seek efficient ways to distribute matrix multiplication task(s) to a set of $N$ distributed servers so that the answers returned from any $R$ servers are…
Many important applications across science, data analytics, and AI workloads depend on distributed matrix multiplication. Prior work has developed a large array of algorithms suitable for different problem sizes and partitionings including…
We consider non-binary product codes with MDS components and their iterative row-column algebraic decoding on the erasure channel. Both independent and block erasures are considered in this paper. A compact graph representation is…
In a distributed storage systems (DSS) with $k$ systematic nodes, robustness against node failure is commonly provided by storing redundancy in a number of other nodes and performing repair mechanism to reproduce the content of the failed…
The concept of space mapping is applied, for the first time, to the design of microwave dispersive delay structures (DDSs). DDSs are components providing specified group delay versus frequency responses for real-time radio systems. The DDSs…
This work presents a theoretical analysis of the probability of successfully retrieving data encoded with MDS codes (e.g., Reed-Solomon codes) in DNA storage systems. We study this probability under independent and identically distributed…
Machine learning (ML) applications become increasingly common in many domains. ML systems to execute these workloads include numerical computing frameworks and libraries, ML algorithm libraries, and specialized systems for deep neural…
Training large machine learning (ML) models with many variables or parameters can take a long time if one employs sequential procedures even with stochastic updates. A natural solution is to turn to distributed computing on a cluster;…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…
Distribution matching is a fixed-length invertible mapping from a uniformly distributed bit sequence to shaped amplitudes and plays an important role in the probabilistic amplitude shaping framework. With conventional constantcomposition…
Over nearly two decades, Differential Dynamic Microscopy (DDM) has become a standard technique for extracting dynamic correlation functions from time-lapse microscopy data, with applications spanning colloidal suspensions, polymer…
Motivation:Microarray experiments result in large scale data sets that require extensive mining and refining to extract useful information. We demonstrate the usefulness of (nonmetric) multidimensional scaling (MDS) method in analyzing a…
The performance gains obtained by large language models (LLMs) are closely linked to their substantial computational and memory requirements. Quantized LLMs offer significant advantages with extremely quantized models, motivating the…
The construction of quantum error-correcting codes (QECCs) with good parameters is a hot topic in the area of quantum information and quantum computing. Quantum maximum distance separable (QMDS) codes are optimal because the minimum…
Convergence of the block iterative method in image reconstruction for positron emission tomography (PET) requires careful control of relaxation parameters, which is a challenging task. The automatic determination of relaxation parameters…
Maximum distance separable (MDS) codes are considered optimal because the minimum distance cannot be improved for a given length and code size. The most prominent MDS codes are likely the generalized Reed-Solomon (GRS) codes. In 1989, Roth…
In block-matching motion estimation (BMME), the search patterns have a significant impact on the algorithm's performance, both the search speed and the search quality. The search pattern should be designed to fit the motion vector…
Decision diagrams (DDs) are a powerful data structure that is used to tackle the state-space explosion problem, not only for discrete systems, but for probabilistic and quantum systems as well. While many of the DDs used in the…