Related papers: Coding for Combined Block-Symbol Error Correction
We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
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…
When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very…
Using convex optimization, we propose entanglement-assisted quantum error correction procedures that are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error correction method achieves…
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction…
In this paper, network error control coding is studied for robust and efficient multicast in a directed acyclic network with imperfect links. The block network error control coding framework, BNEC, is presented and the capability of the…
Error correction, in the standard meaning of the term, implies the ability to correct all small analog errors and some large errors. Examining assumptions at the basis of the recently proposed quantum error-correcting codes, it is pointed…
A simple algorithm for decoding both errors and erasures of Reed-Solomon codes is described.
Low complexity error correction code is a key enabler for next generation ultra-reliable low-latency communications (xURLLC) in six generation (6G). Against this background, this paper proposes a decoding scheme for linear block code by…
Continuous-variable systems protected by bosonic quantum error-correcting codes have emerged as a promising platform for quantum information processing. To date, design of codewords has centered on optimizing the occupation of basis states…
This letter introduces a novel channel coding design framework for short-length codewords that permits balancing the tradeoff between the bit error rate floor and waterfall region by modifying a single real-valued parameter. The proposed…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
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…
A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so called crossbar…
Practical random network coding based schemes for multicast include a header in each packet that records the transformation between the sources and the terminal. The header introduces an overhead that can be significant in certain…
Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been…
Inspired by Knill's scheme for message passing error detection, here we develop a scheme for message passing error correction for the nine-qubit Bacon-Shor code. We show that for two levels of concatenated error correction, where classical…
The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure,…