Related papers: A New Class of Geometric Analog Error Correction C…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
Quantum error correction (QEC) is crucial for realizing scalable quantum technologies, and topological quantum error correction (TQEC) has emerged as the most experimentally advanced paradigm of QEC. Existing homological and topological…
We consider $t$-Lee-error-correcting codes of length $n$ over the residue ring $\mathbb{Z}_m := \mathbb{Z}/m\mathbb{Z}$ and determine upper and lower bounds on the number of $t$-Lee-error-correcting codes. We use two different methods,…
In continuation to an earlier work, where error exponents of typical random codes were studied in the context of general block coding, with no underlying structure, here we carry out a parallel study on typical random, time-varying trellis…
Block codes, which correct asymmetric errors with limited-magnitude, are studied. These codes have been applied recently for error correction in flash memories. The codes will be represented by lattices and the constructions will be based…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…
In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduce redundancy to ensure recoverability from failure. To get the most out of every byte, practitioners and theorists have…
We derive a convex optimization problem for the task of segmenting sequential data, which explicitly treats presence of outliers. We describe two algorithms for solving this problem, one exact and one a top-down novel approach, and we…
We consider the problem of transmission of a sequence of real data produced by a Nyquist sampled band-limited analog source over a band-limited analog channel, which introduces an additive white Gaussian noise. An analog coding scheme is…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
Outlier or anomaly detection is an important task in data analysis. We discuss the problem from a geometrical perspective and provide a framework that exploits the metric structure of a data set. Our approach rests on the manifold…
High-dimensional data poses unique challenges in outlier detection process. Most of the existing algorithms fail to properly address the issues stemming from a large number of features. In particular, outlier detection algorithms perform…
Outlier detection is an important topic in machine learning and has been used in a wide range of applications. In this paper, we approach outlier detection as a binary-classification issue by sampling potential outliers from a uniform…
This work continues the study of linear error correcting codes against adversarial insertion deletion errors (insdel errors). Previously, the work of Cheng, Guruswami, Haeupler, and Li \cite{CGHL21} showed the existence of asymptotically…
Recent studies identify that Deep learning Neural Networks (DNNs) are vulnerable to subtle perturbations, which are not perceptible to human visual system but can fool the DNN models and lead to wrong outputs. A class of adversarial attack…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Outlier detection aims to identify unusual data instances that deviate from expected patterns. The outlier detection is particularly challenging when outliers are context dependent and when they are defined by unusual combinations of…
Binary memristive crossbars have gained huge attention as an energy-efficient deep learning hardware accelerator. Nonetheless, they suffer from various noises due to the analog nature of the crossbars. To overcome such limitations, most…
In this paper, an algorithm for construction of multiple sets of two dimensional (2D) or matrix unipolar (optical) orthogonal codes has been proposed. Representations of these 2D codes in difference of positions representation (DoPR) have…
Quantum error correction is essential for robust quantum information processing with noisy devices. As bosonic quantum systems play a crucial role in quantum sensing, communication, and computation, it is important to design error…