Related papers: On Metrics for Error Correction in Network Coding
Error-correcting codes are usually envisioned to counter errors by operating unitary corrections depending on the projective measurement results of some syndrome observables. We here propose a way to use them in a more integrated way, where…
While network coding can be an efficient means of information dissemination in networks, it is highly susceptible to "pollution attacks," as the injection of even a single erroneous packet has the potential to corrupt each and every packet…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
Random linear network coding (RLNC) provides a powerful framework for non-coherent communication, where reliable transmission requires correcting errors and erasures induced by network mixing and motivates the use of subspace codes. In this…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
Unary coding has found applications in data compression, neural network training, and in explaining the production mechanism of birdsong. Unary coding is redundant; therefore it should have inherent error correction capacity. An expression…
This paper investigates achievable information rates and error exponents of mismatched decoding when the channel belongs to the class of channels that are close to the decoding metric in terms of relative entropy. For both discrete- and…
This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the…
The secrecy capacity of a network, for a given collection of permissible wiretap sets, is the maximum rate of communication such that observing links in any permissible wiretap set reveals no information about the message. This paper…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
The growing demand for highly reliable communication systems drives the research and development of algorithms that identify and correct errors during data transmission and storage. This need becomes even more critical in hard-to-access or…
We investigate linear network coding in the context of robust function computation, where a sink node is tasked with computing a target function of messages generated at multiple source nodes. In a previous work, a new distance measure was…
Background: When using deep learning models, there are many possible vulnerabilities and some of the most worrying are the adversarial inputs, which can cause wrong decisions with minor perturbations. Therefore, it becomes necessary to…
Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
An error correcting code using a tree-like multilayer perceptron is proposed. An original message $\mbi{s}^0$ is encoded into a codeword $\boldmath{y}_0$ using a tree-like committee machine (committee tree) or a tree-like parity machine…
In recent years, network coding has become one of the most interesting fields and has attracted considerable attention from both industry and academia. The idea of network coding is based on the concept of allowing intermediate nodes to…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…