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Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental problem in coding theory and practice is to efficiently decode the received word…
Large-scale systems with arrays of solid state disks (SSDs) have become increasingly common in many computing segments. To make such systems resilient, we can adopt erasure coding such as Reed-Solomon (RS) code as an alternative to…
The extended Euclidean algorithm (EEA) for polynomial greatest common divisors is commonly used in solving the key equation in the decoding of Reed-Solomon (RS) codes, and more generally in BCH decoding. For this particular application, the…
In this paper we provide a detailed description of Reed-Solomon (RS) codes, the most important algorithms for decoding them, and their use in concatenated coding systems for space applications. In the current literature there is scattered…
In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is…
In this paper, we address the node repair problem of Reed-Solomon (RS) coded distributed storage systems. Specifically, to overcome the challenges of multiple-node failures of RS codes under the rack-aware storage model, we employ good…
Array codes have been widely employed in storage systems, such as Redundant Arrays of Inexpensive Disks (RAID). The row-diagonal parity (RDP) codes and EVENODD codes are two popular double-parity array codes. As the capacity of hard disks…
Generalized Concatenated codes are a code construction consisting of a number of outer codes whose code symbols are protected by an inner code. As outer codes, we assume the most frequently used Reed-Solomon codes; as inner code, we assume…
Modern spacecraft communication systems rely on concatenated error correction schemes, typically combining convolutional and Reed-Solomon (RS) codes. This paper presents a decoder-side method that uses a machine learning model to estimate…
Because of their importance in applications and their quite simple definition, Reed-Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed-Solomon codes are far from being simple…
Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they coincide with Reed-Solomon codes (Hamming metric) and Gabidulin codes (rank…
The sum-rank metric is a hybrid between the Hamming metric and the rank metric and suitable for error correction in multishot network coding and distributed storage as well as for the design of quantum-resistant cryptosystems. In this work,…
Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the…
Folded Reed-Solomon (FRS) codes are a well-studied family of codes, known for achieving list decoding capacity. In this work, we give improved deterministic and randomized algorithms for list decoding FRS codes of rate $R$ up to radius…
The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate…
Minimum storage regenerating (MSR) codes are MDS codes which allow for recovery of any single erased symbol with optimal repair bandwidth, based on the smallest possible fraction of the contents downloaded from each of the other symbols.…
We study covering problems in Hamming and Grassmann spaces through a unified coding-theoretic and information-theoretic framework. Viewing covering as a form of quantization in general metric spaces, we introduce the notion of the average…
This study addresses the use of Reed-Solomon error correction codes in QR codes to enhance resilience against failures. To fully grasp this approach, a basic cryptographic context is provided, necessary for understanding Reed-Solomon codes.…
Maximum distance separable (MDS) array codes constitute an important class of error-correcting codes due to their optimal distance properties and their relevance in distributed storage systems. In this paper, we investigate the construction…
Erasure codes provide a storage efficient alternative to replication based redundancy in (networked) storage systems. They however entail high communication overhead for maintenance, when some of the encoded fragments are lost and need to…