Related papers: Collaborative Decoding of Interleaved Reed-Solomon…
Identification is a communication paradigm that promises exponential advantages over transmission for applications that do not actually require all messages to be reliably transmitted. Notably, the identification capacity theorems prove…
Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides…
In this work it is shown that locally repairable codes (LRCs) can be list-decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error-correction capabilities. The corresponding decoding radius…
We introduce Reed-Solomon-Gabidulin codes which is, at the same time, an extension to Reed-Solomon codes on the one hand and Gabidulin codes on the other hand. We prove that our codes have good properties with respect to the minimal…
This paper proposes a new class of multi-dimensional nonsystematic Reed-Solomon codes that are constructed based on the multi-dimensional Fourier transform over a finite field. The proposed codes are the extension of the nonsystematic…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
We explore connections between secret sharing and secret key agreement, which yield a simple and scalable multiterminal key agreement protocol. In our construction, we use error-correcting codes, specifically Reed-Solomon codes with…
A new interpolation-based decoding principle for interleaved Gabidulin codes is presented. The approach consists of two steps: First, a multi-variate linearized polynomial is constructed which interpolates the coefficients of the received…
Generalized Concatenated (GC), also known as Integrated Interleaved (II) Codes, are studied from an erasure correction point of view making them useful for Redundant Arrays of Independent Disks (RAID) types of architectures combining global…
List-decoding of Reed-Solomon (RS) codes beyond the so called Johnson radius has been one of the main open questions since the work of Guruswami and Sudan. It is now known by the work of Rudra and Wootters, using techniques from high…
In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless,…
This work presents a theoretical analysis of the probability of successfully retrieving data encoded with MDS codes (e.g., Reed-Solomon codes) in DNA storage systems. We study this probability under independent and identically distributed…
Motivated by applications of distributed storage systems to cloud-based key-value stores, the multi-version coding problem has been recently formulated to efficiently store frequently updated data in asynchronous decentralized storage…
A locally recoverable code is an error-correcting code such that any erasure in a coordinate of a codeword can be recovered from a set of other few coordinates. In this article we introduce a model of local recoverable codes that also…
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…
Several types of AL-FEC (Application-Level FEC) codes for the Packet Erasure Channel exist. Random Linear Codes (RLC), where redundancy packets consist of random linear combinations of source packets over a certain finite field, are a…
An unconventional encoding scheme called concurrent coding, has recently been demonstrated and shown to offer interesting features and benefits in comparison to conventional techniques, e.g. robustness against burst errors and improved…
By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality…
The material in this book is presented to graduate students in Information and Communication theory. The idea is that we give an introduction to particular applications of information theory and coding in digital communications. The goal is…
Distributed storage systems for large clusters typically use replication to provide reliability. Recently, erasure codes have been used to reduce the large storage overhead of three-replicated systems. Reed-Solomon codes are the standard…