Related papers: Synchronization Strings and Codes for Insertions a…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
Motivated by applications in DNA-based storage and communication systems, we study deletion and insertion errors simultaneously in a burst. In particular, we study a type of error named $t$-deletion-$s$-insertion-burst ($(t,s)$-burst for…
Motivated by applications in DNA storage, we study a setting in which strings are affected by tandem-duplication errors. In particular, we look at two settings: disjoint tandem-duplication errors, and equal-length tandem-duplication errors.…
Much progress has been made on decoding algorithms for error-correcting codes in the last decade. In this article, we give an introduction to some fundamental results on iterative, message-passing algorithms for low-density parity check…
The ability to detect failures and anomalies are fundamental requirements for building reliable systems for computer vision applications, especially safety-critical applications of semantic segmentation, such as autonomous driving and…
Measuring similarities between strings is central for many established and fast growing research areas including information retrieval, biology, and natural language processing. The traditional approach for string similarity measurements is…
This paper studies reconstruction of strings based upon their substrings spectrum. Under this paradigm, it is assumed that all substrings of some fixed length are received and the goal is to reconstruct the string. While many existing works…
Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, the quantum synchronizable codes…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
In this paper, we study how often unique decoding from $t$ insertions or $t$ deletions occurs for error correcting codes. Insertions and deletions frequently occur in synchronization problems and DNA, a medium which is beginning to be used…
Historically, scalability has been a major challenge to the successful application of semidefinite programming in fields such as machine learning, control, and robotics. In this paper, we survey recent approaches for addressing this…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
Insertion and deletion (insdel for short) errors are synchronization errors in communication systems caused by the loss of positional information in the message. Reed-Solomon codes have gained a lot of interest due to its encoding…
Sparse representations of images are useful in many computer vision applications. Sparse coding with an $l_1$ penalty and a learned linear dictionary requires regularization of the dictionary to prevent a collapse in the $l_1$ norms of the…
We describe and explore so-called linear hash functions and show how they can be used to build error detection and correction codes. The method can be applied for different types of errors (for example, burst errors). When the method is…
Archival information systems in government agency is one of the most used applications for daily acitivities. One feature in application management information document is searching. This feature serves to search for documents from a…
Permutation codes were extensively studied in order to correct different types of errors for the applications on power line communication and rank modulation for flash memory. In this paper, we introduce the neural network decoders for…
Distributed data storage systems are essential to deal with the need to store massive volumes of data. In order to make such a system fault-tolerant, some form of redundancy becomes crucial, incurring various overheads - most prominently in…
Synchronization problem for linear coupled networks is a hot topic in recent decade. However, until now, some confused concepts and results still puzzle people. To avoid further misleading researchers, it is necessary to point out these…
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that,…