Related papers: Combining subspace codes with classical linear err…
A fundamental requirement for enabling fault-tolerant quantum information processing is an efficient quantum error-correcting code (QECC) that robustly protects the involved fragile quantum states from their environment. Just as classical…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
This work considers the smart repeater network where a single source $s$ wants to send two independent packet streams to destinations $\{d_1,d_2\}$ with the help of relay $r$. The transmission from $s$ or $r$ is modeled by packet erasure…
In this paper, we show that the Advanced Encryption Standard (AES) cryptosystem can be used as an error-correcting code to obtain reliability over noisy communication and data systems. Moreover, we characterize a family of computational…
Pseudocode is extensively used in introductory programming courses to instruct computer science students in algorithm design, utilizing natural language to define algorithmic behaviors. This learning approach enables students to convert…
Employing underlying geometric and algebraic structures allows for constructing bespoke codes for local recovery of erasures. We survey techniques for enriching classical codes with additional machinery, such as using lines or curves in…
We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and…
A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as…
We consider network coding for a noiseless broadcast channel where each receiver demands a subset of messages available at the transmitter and is equipped with noisy side information in the form an erroneous version of the message symbols…
Modern 5G communication systems implement a combination of error correction and feedback-based erasure correction (HARQ/ARQ) as reliability mechanisms, which can introduce substantial delay and resource inefficiency. We propose forward…
Surface codes are among the best candidates to ensure the fault-tolerance of a quantum computer. In order to avoid the accumulation of errors during a computation, it is crucial to have at our disposal a fast decoding algorithm to quickly…
The persistent storage of big data requires advanced error correction schemes. The classical approach is to use error correcting codes (ECCs). This work studies an alternative approach, which uses the redundancy inherent in data itself for…
Erasure list decoding was introduced to correct a larger number of erasures with output of a list of possible candidates. In the present paper, we consider both random linear codes and algebraic geometry codes for list decoding erasure…
We consider an ensemble of constant composition codes that are subsets of linear codes: while the encoder uses only the constant-composition subcode, the decoder operates as if the full linear code was used, with the motivation of…
A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name of quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
In this paper, we consider the iterative method of subspace corrections with random ordering. We prove identities for the expected convergence rate, which can provide sharp estimates for the error reduction per iteration. We also study the…
Codes in the projective space and codes in the Grassmannian over a finite field - referred to as subspace codes and constant-dimension codes (CDCs), respectively - have been proposed for error control in random linear network coding. For…
DNA storage has emerged as a promising solution for large-scale and long-term data preservation. Among various error types, insertions are the most frequent errors occurring in DNA sequences, where the inserted symbol is often identical or…
In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. We study the decoding problem using the state space description and this…