Related papers: Generalized Concatenated Types of Codes for Erasur…
A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it…
We present the construction of a family of erasure correcting codes for distributed storage that achieve low repair bandwidth and complexity at the expense of a lower fault tolerance. The construction is based on two classes of codes, where…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a…
Graph clustering aims to divide the graph into different clusters. The recently emerging deep graph clustering approaches are largely built on graph neural networks (GNN). However, GNN is designed for general graph encoding and there is a…
We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted…
Some combinatorial designs, such as Hadamard matrices, have been extensively researched and are familiar to readers across the spectrum of Science and Engineering. They arise in diverse fields such as cryptography, communication theory, and…
Concatenation is a method of building long codes out of shorter ones, it attempts to meet the problem of decoding complexity by breaking the required computation into manageable segments. Concatenated Continuous Phase Frequency Shift Keying…
Coding theoretic approached have been developed to significantly reduce the communication load in modern distributed computing system. In particular, coded distributed computing (CDC) introduced by Li et al. can efficiently trade…
Computational storage, known as a solution to significantly reduce the latency by moving data-processing down to the data storage, has received wide attention because of its potential to accelerate data-driven devices at the edge. To meet…
Noisy shuffling channels capture the main characteristics of DNA storage systems where distinct segments of data are received out of order, after being corrupted by substitution errors. For realistic schemes with short-length segments,…
CRC codes have long since been adopted in a vast range of applications. The established notion that they are suitable primarily for error detection can be set aside through use of the recently proposed Guessing Random Additive Noise…
A novel coding scheme for exact repair-regenerating codes is presented in this paper. The codes proposed in this work can trade between the repair bandwidth of nodes (number of downloaded symbols from each surviving node in a repair…
Motivated by iterative decoding techniques for the binary erasure channel Hollmann and Tolhuizen introduced and studied the notion of generic erasure correcting sets for linear codes. A generic $(r,s)$--erasure correcting set generates for…
This paper proposes an erasure correcting code and its systematic form for the distributed storage system. The proposed codes are encoded by exclusive OR and bit-level shift operation. By the shift operation, the encoded packets are…
We introduce generalized function-correcting partition codes (GFCPCs) that simultaneously protect multiple partitions of the message space against different numbers of errors. Given partitions with respective distance requirements, a GFCPC…
Manifold matching works to identify embeddings of multiple disparate data spaces into the same low-dimensional space, where joint inference can be pursued. It is an enabling methodology for fusion and inference from multiple and massive…
This thesis makes several significant contributions to the theory of both Regenerating (RG) and Locally Recoverable (LR) codes. The two principal contributions are characterizing the optimal rate of an LR code designed to recover from $t$…
Graph condensation (GC) has gained significant attention for its ability to synthesize smaller yet informative graphs. However, existing studies often overlook the robustness of GC in scenarios where the original graph is corrupted. In such…
We consider high-dimensional generalized linear models when the covariates are contaminated by measurement error. Estimates from errors-in-variables regression models are well-known to be biased in traditional low-dimensional settings if…