Related papers: Equivalence of Insertion/Deletion Correcting Codes…
A method to combine two quantum error-correcting codes is presented. Even when starting with additive codes, the resulting code might be non-additive. Furthermore, the notion of the erasure space is introduced which gives a full…
In this paper we construct multidimensional codes with high dimension. The codes can correct high dimensional errors which have the form of either small clusters, or confined to an area with a small radius. We also consider small number of…
Embeddings mapping high-dimensional discrete input to lower-dimensional continuous vector spaces have been widely adopted in machine learning applications as a way to capture domain semantics. Interviewing 13 embedding users across…
Considerable interest has been paid in recent literature to codes combining local and global properties for erasure correction. Applications are in cloud type of implementations, in which fast recovery of a failed storage device is…
Several measures exist for string similarity, including notable ones like the edit distance and the indel distance. The former measures the count of insertions, deletions, and substitutions required to transform one string into another,…
The problem of error-control in random linear network coding is considered. A ``noncoherent'' or ``channel oblivious'' model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer…
Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic…
In this paper, we investigate the problem of designing $(n, N; \mathcal{B})$-reconstruction codes for $N\in \{14,11,9,5\}$, where $\mathcal{B}$ is the single-deletion single-substitution ball function that maps a sequence to the set of all…
Dense retrieval, which encodes queries and documents into a single dense vector, has become the dominant neural retrieval approach due to its simplicity and compatibility with fast approximate nearest neighbor algorithms. As the tasks dense…
In this paper, we introduce a model of a single-failure locally recoverable distributed storage system. This model appears to give rise to a problem seemingly dual of the well-studied index coding problem. The relation between the…
We present the construction of a new family of erasure correcting codes for distributed storage that yield low repair bandwidth and low repair complexity. The construction is based on two classes of parity symbols. The primary goal of the…
Neural networks are prone to overfitting and memorizing data patterns. To avoid over-fitting and enhance their generalization and performance, various methods have been suggested in the literature, including dropout, regularization, label…
We construct deletion error-correcting codes in the oblivious model, where errors are adversarial but oblivious to the encoder's randomness. Oblivious errors bridge the gap between the adversarial and random error models, and are motivated…
Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a…
We discuss how subspace codes can be used to simultaneously correct errors and erasures when the network performs random linear network coding and the edges are noisy channels. This is done by combining the subspace code with a classical…
Non-binary codes correcting multiple deletions have recently attracted a lot of attention. In this work, we focus on multiplicity-free codes, a family of non-binary codes where all symbols are distinct. Our main contribution is a new…
Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…
For an $(n,k,\ell)$ MDS array code over $\mathbb{F}_q$, how small can the repair bandwidth and repair I/O be under linear exact repair? We study this question in the regime where the field size $q$, the redundancy $r=n-k$, and the…
Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving…
Folding a sequence $S$ into a multidimensional box is a method that is used to construct multidimensional codes. The well known operation of folding is generalized in a way that the sequence $S$ can be folded into various shapes. The new…