Related papers: On Metrics for Error Correction in Network Coding
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…
In rank-metric cryptography, a vector from a finite dimensional linear space over a finite field is viewed as the linear space spanned by its entries. The rank decoding problem which is the analogue of the problem of decoding a random…
In this work we study zero vs. epsilon-error capacity in network coding instances. For multicast network coding it is well known that all rates that can be delivered with arbitrarily small error probability can also be delivered with zero…
Is perfect error correction always worth the trouble? A framework is presented for the analysis of error detection and correction in multi-level systems of communication that takes into account degrees of freedom attended and ignored by…
We consider communication over a noisy network under randomized linear network coding. Possible error mechanism include node- or link- failures, Byzantine behavior of nodes, or an over-estimate of the network min-cut. Building on the work…
In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable of…
It is well known that a determined adversary can fool a neural network by making imperceptible adversarial perturbations to an image. Recent studies have shown that these perturbations can be detected even without information about the…
We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…
Error correction code is a major part of the communication physical layer, ensuring the reliable transfer of data over noisy channels. Recently, neural decoders were shown to outperform classical decoding techniques. However, the existing…
We consider distance functions on a quotient module $M/K$ induced by distance functions on a module $M$. We define error-correction for codes in $M/K$ with respect to induced distance functions. For the case that the metric is induced by a…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
This paper considers the problem of error correction for a cooperative data exchange (CDE) system, where some clients are compromised or failed and send false messages. Assuming each client possesses a subset of the total messages, we…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
In this work we present error-correcting codes for random network coding based on rank- metric codes, Ferrers diagrams, and puncturing. For most parameters, the constructed codes are larger than all previously known codes.
Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the…
Joint network-channel codes (JNCC) can improve the performance of communication in wireless networks, by combining, at the physical layer, the channel codes and the network code as an overall error-correcting code. JNCC is increasingly…
Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions. In this work, we investigate the…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…
We present a study on connection errors in networks of linear features and methods of error detection. We model networks with special connection specifications as networks with hierarchically connected features and define errors considering…