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Coordinate transformation models often fail to account for nonlinear and spatially dependent distortions, leading to significant residual errors in geospatial applications. Here we propose a residual-based neural correction strategy, in…
The explosion of the amount of data stored in cloud systems calls for more efficient paradigms for redundancy. While replication is widely used to ensure data availability, erasure correcting codes provide a much better trade-off between…
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
Residue codes have been traditionally used for compute error correction rather than storage error correction. In this paper, we use these codes for storage error correction with surprising results. We find that adapting residue codes to…
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment.…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
Resilient algorithms in high-performance computing are subject to rigorous non-functional constraints. Resiliency must not increase the runtime, memory footprint or I/O demands too significantly. We propose a task-based soft error detection…
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
This study investigates the capabilities of Cyclic Redundancy Checks(CRCs) to detect burst and random errors. Researchers have favored these error detection codes throughout the evolution of computing and have implemented them in…
A novel correction algorithm is proposed for multi-class classification problems with corrupted training data. The algorithm is non-intrusive, in the sense that it post-processes a trained classification model by adding a correction…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…
This paper investigates polynomial remainder codes with non-pairwise coprime moduli. We first consider a robust reconstruction problem for polynomials from erroneous residues when the degrees of all residue errors are assumed small, namely…
Quantum computation is a subject of much theoretical promise, but has not been realized in large scale, despite the discovery of fault-tolerant procedures to overcome decoherence. Part of the reason is that the theoretically modest…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
Cyclic redundancy check (CRC) codes check if a codeword is correctly received. This paper presents an algorithm to design CRC codes that are optimized for the code-specific error behavior of a specified feedforward convolutional code. The…
Backtracking (i.e., reverse execution) helps the user of a debugger to naturally think backwards along the execution path of a program, and thinking backwards makes it easy to locate the origin of a bug. So far backtracking has been…