Related papers: Recursive Code Construction for Random Networks

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.

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 this paper, we present a coding-theoretic framework for message transmission over packet-switched networks. Network is modeled as a channel which can induce packet errors, deletions, insertions, and out of order delivery of packets. The…

In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…

As a strategy to further reduce the transmission pressure during the peak traffic times in wireless network, coded caching has been widely studied recently. And several coded caching schemes are constructed focusing on the two core problems…

While random linear network coding is a powerful tool for disseminating information in communication networks, it is highly susceptible to errors caused by various sources. Due to error propagation, errors greatly deteriorate the throughput…

Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…

Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…

Subspace codes were introduced by K\"otter and Kschischang for error control in random linear network coding. In this paper, a layered type of subspace codes is considered, which can be viewed as a superposition of multiple component…

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…

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…

This paper considers quantum network coding, which is a recent technique that enables quantum information to be sent on complex networks at higher rates than by using straightforward routing strategies. Kobayashi et al. have recently showed…

As the mobile application landscape expands, wireless networks are tasked with supporting various connection profiles, including real-time communications and delay-sensitive traffic. Among many ensuing engineering challenges is the need to…

In this paper, we study three applications of recursion to problems in coding and random permutations. First, we consider locally recoverable codes with partial locality and use recursion to estimate the minimum distance of such codes. Next…

We develop novel protocols for generating loss-tolerant quantum codes; these are central for safeguarding information against qubit losses, with most crucial applications in quantum communications. Contrary to current proposals, our method…

Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…

We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. 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…

Network coding is known to improve the throughput and the resilience to losses in most network scenarios. In a practical network scenario, however, the accurate modeling of the traffic is often too complex and/or infeasible. The goal is…

We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted…