Related papers: Locally Recoverable codes from rational maps
We continue the investigation of locally testable codes, i.e., error-correcting codes for whom membership of a given word in the code can be tested probabilistically by examining it in very few locations. We give two general results on…
We prove that a class of distance-optimal local reconstruction codes (LRCs), an important family of repair-efficient codes for distributed storage systems, achieve the maximum distance separable private information retrieval capacity for…
We present a novel approach to image restoration that leverages ideas from localized structured prediction and non-linear multi-task learning. We optimize a penalized energy function regularized by a sum of terms measuring the distance…
In this letter, locally recoverable codes with maximal recoverability are studied with a focus on identifying the MDS codes resulting from puncturing and shortening. By using matroid theory and the relation between MDS codes and uniform…
We develop reconstruction schemes to determine penetrable obstacles in a region of \mathbb{R}^{2} or \mathbb{R}^{3} and we consider anisotropic elliptic equations. This algorithm uses oscillating-decaying solutions to the equation. We apply…
We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…
In this paper, the design of irregular turbo codes for the binary erasure channel is investigated. An analytic expression of the erasure probability of punctured recursive systematic convolutional codes is derived. This exact expression…
Local fixpoint iteration describes a technique that restricts fixpoint iteration in function spaces to needed arguments only. It has been studied well for first-order functions in abstract interpretation and also in model checking. Here we…
In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. This local-global construction is motivated by practical applications in data storage and transmission where reduced-latency…
This paper employs a localized orthogonal decomposition (LOD) method with $H^1$ interpolation for solving the multiscale elliptic problem. This method does not need any assumptions on scale separation. We give a priori error estimate for…
Nonlinear inverse problems often trade inexpensive but fragile first-order updates against curvature-aware methods such as Gauss-Newton and Levenberg-Marquardt, which obtain stronger directions by repeatedly solving Jacobian-based…
When attempting to recover functions from observational data, one naturally seeks to do so in an optimal manner with respect to some modeling assumption. With a focus put on the worst-case setting, this is the standard goal of Optimal…
Lifted Reed-Solomon codes, introduced by Guo, Kopparty and Sudan in 2013, are known as one of the few families of high-rate locally correctable codes. They are built through the evaluation over the affine space of multivariate polynomials…
We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the…
As the most essential part of CAD modeling operations, boolean operations on B-rep CAD models often suffer from errors. Errors caused by geometric precision or numerical uncertainty are hard to eliminate. They will reduce the reliability of…
A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches…
A major issue of locally repairable codes is their robustness. If a local repair group is not able to perform the repair process, this will result in increasing the repair cost. Therefore, it is critical for a locally repairable code to…
Exact-repair regenerating codes are considered for the case (n,k,d)=(4,3,3), for which a complete characterization of the rate region is provided. This characterization answers in the affirmative the open question whether there exists a…