Related papers: A New Class of Geometric Analog Error Correction C…
In many applications, when building linear regression models, it is important to account for the presence of outliers, i.e., corrupted input data points. Such problems can be formulated as mixed-integer optimization problems involving cubic…
This paper considers the problem of code design for a channel where communications and radar systems coexist, modeled as having both Additive White Gaussian Noise (AWGN) and Additive Radar Interference (ARI). The issue of how to adapt or…
A brain can detect outlier just by using only normal samples. Similarly, one-class classification (OCC) also uses only normal samples to train the model and trained model can be used for outlier detection. In this paper, a multi-layer…
The memristor is promising to be the basic cell of next-generation computation systems. Compared to the traditional MOSFET device, the memristor is efficient over energy and area. But one of the biggest challenges faced with researchers is…
The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as…
Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of…
Concatenation of two quantum error correcting codes with complementary sets of transversal gates can provide a means towards universal fault-tolerant computation. We first show that it is generally preferable to choose the inner code with…
Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
Outlier detection is one of the most important processes taken to create good, reliable data in machine learning. The most methods of outlier detection leverage an auxiliary reconstruction task by assuming that outliers are more difficult…
Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains…
This paper provides a mathematical analysis of optimal algebraic manipulation detection (AMD) codes. We prove several lower bounds on the success probability of an adversary and we then give some combinatorial characterizations of AMD codes…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
We propose a two-layer coding architecture for communication of multiple users over a shared slotted medium enabling joint collision resolution and decoding. Each user first encodes its information bits with an outer code for reliability,…
Edge computing is emerging as a new paradigm to allow processing data at the edge of the network, where data is typically generated and collected, by exploiting multiple devices at the edge collectively. However, exploiting the potential of…
The growing demand for highly reliable communication systems drives the research and development of algorithms that identify and correct errors during data transmission and storage. This need becomes even more critical in hard-to-access or…