Related papers: Generalized Concatenated Types of Codes for Erasur…
Distributed storage systems support failures of individual devices by the use of replication or erasure correcting codes. While erasure correcting codes offer a better storage efficiency than replication for similar fault tolerance, they…
Modern large-scale distributed storage systems use erasure codes to protect against node failures with low storage overhead. In practice, the failure rate and other factors of storage devices in the system may vary significantly over time,…
Erasure coding with wide stripes is increasingly adopted to reduce storage overhead in large-scale storage systems. However, existing Locally Repairable Codes (LRCs) exhibit structural limitations in this setting: inflated local groups…
Two concatenated coding schemes incorporating algebraic Reed-Solomon (RS) codes and polarization-adjusted convolutional (PAC) codes are proposed. Simulation results show that at a bit error rate of $10^{-5}$, a concatenated scheme using RS…
We introduce a new family of erasure codes, called group decodable code (GDC), for distributed storage system. Given a set of design parameters {\alpha; \beta; k; t}, where k is the number of information symbols, each codeword of an…
In this paper, we propose a new coded computing technique called "substitute decoding" for general iterative distributed computation tasks. In the first part of the paper, we use PageRank as a simple example to show that substitute decoding…
We introduce a novel framework for implementing error-correction in constrained systems. The main idea of our scheme, called Quantized-Constraint Concatenation (QCC), is to employ a process of embedding the codewords of an error-correcting…
We introduce and analyze a new type of decoding algorithm called General Color Clustering (GCC), based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under code capacity…
The rapid growth of graph data poses significant challenges in storage, transmission, and particularly the training of graph neural networks (GNNs). To address these challenges, graph condensation (GC) has emerged as an innovative solution.…
Generalized Category Discovery (GCD) aims to classify unlabeled data containing both seen and novel categories. Although existing methods perform well on generic datasets, they struggle in fine-grained scenarios. We attribute this…
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
Goppa Codes are a well-known class of codes with, among others, applications in code-based cryptography. In this paper, we present a collaborative decoding algorithm for interleaved Goppa codes (IGC). Collaborative decoding increases the…
We consider the problem of constructing codes that can correct $\delta$ deletions occurring in an arbitrary binary string of length $n$ bits. Varshamov-Tenengolts (VT) codes can correct all possible single deletions $(\delta=1)$ with an…
Motivated by an application to database linear querying, such as private information-retrieval protocols, we suggest a fundamental property of linear codes -- the generalized covering radius. The generalized covering-radius hierarchy of a…
The interpolation-based decoding that was developed for general evaluation AG codes is shown to be equally applicable to general differential AG codes. A performance analysis of the decoding algorithm, which is parallel to that of its…
In this work, we introduce a new concatenation scheme which aims at protecting information against the occurrence of both computational errors and quantum erasures. According to our scheme, the internal code must be a quantum…
Linear inverse problems are ubiquitous in various science and engineering disciplines. Of particular importance in the past few decades, is the incorporation of sparsity based priors, in particular $\ell_1$ priors, into linear inverse…
International Classification of Diseases (ICD) are the de facto codes used globally for clinical coding. These codes enable healthcare providers to claim reimbursement and facilitate efficient storage and retrieval of diagnostic…
Unsourced random access (URA) has emerged as a pragmatic framework for next-generation distributed sensor networks. Within URA, concatenated coding structures are often employed to ensure that the central base station can accurately recover…
Content-invariance in mapping codes learned by GAEs is a useful feature for various relation learning tasks. In this paper we show that the content-invariance of mapping codes for images of 2D and 3D rotated objects can be substantially…