Related papers: Reconstructing Reed-Solomon Codes from Multiple No…
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.…
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…
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 letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbol-wise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
The performance of the information reconciliation phase is crucial for quantum key distribution (QKD). Reverse reconciliation (RR) is typically preferred over direct reconciliation (DR) because it yields higher secure key rates. However, a…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbolwise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to…
Vector symbolic architectures (VSAs) are a family of information representation techniques which enable composition, i.e., creating complex information structures from atomic vectors via binding and superposition, and have recently found…
Noisy shuffling channels capture the main characteristics of DNA storage systems where distinct segments of data are received out of order, after being corrupted by substitution errors. For realistic schemes with short-length segments,…
The sequence reconstruction problem for insertion/deletion channels has attracted significant attention owing to their applications recently in some emerging data storage systems, such as racetrack memories, DNA-based data storage. Our goal…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads…
The paper considers coding schemes derived from Reed-Muller (RM) codes, for transmission over input-constrained memoryless channels. Our focus is on the $(d,\infty)$-runlength limited (RLL) constraint, which mandates that any pair of…
Quantum noise is currently limiting efficient quantum information processing and computation. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using…
We consider the problem of signal reconstruction for a system under sparse signal corruption by a malicious agent. The reconstruction problem follows the standard error coding problem that has been studied extensively in the literature. We…
A modification of Koetter-Kschischang codes for random networks is presented (these codes were also studied by Wang et al. in the context of authentication problems). The new codes have higher information rate, while maintaining the same…
The complexity of maximal likelihood decoding of the Reed-Solomon codes $[q-1, k]_q$ is a well known open problem. The only known result in this direction states that it is at least as hard as the discrete logarithm in some cases where the…
Quantum error correction codes based on continuous variables play an important role for the implementation of quantum communication systems. A natural application of such codes occurs within quantum repeater systems which are used to combat…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…