Related papers: Reliable and Secure Multishot Network Coding using…
We propose a simple yet effective wireless network coding and decoding technique. It utilizes spatial diversity through cooperation between nodes which carry out distributed encoding operations dictated by generator matrices of linear block…
Non-malleable codes are fundamental objects at the intersection of cryptography and coding theory. These codes provide security guarantees even in settings where error correction and detection are impossible, and have found applications to…
In this paper we provide a detailed description of Reed-Solomon (RS) codes, the most important algorithms for decoding them, and their use in concatenated coding systems for space applications. In the current literature there is scattered…
For communication systems with heavy burst noise, an optimal Forward Error Correction (FEC) scheme is expected to have a large burst error correction capacity while simultaneously owning moderate random error correction capability. This…
Power decoding, or "decoding by virtual interleaving", of Reed--Solomon codes is a method for unique decoding beyond half the minimum distance. We give a new variant of the Power decoding scheme, building upon the key equation of Gao. We…
Insertion and deletion (insdel for short) errors are synchronization errors in communication systems caused by the loss of positional information in the message. Reed-Solomon codes have gained a lot of interest due to its encoding…
In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to…
We introduce a discrete network corresponding to any Gaussian wireless network that is obtained by simply quantizing the received signals and restricting the transmitted signals to a finite precision. Since signals in the discrete network…
We consider the random linear precoder at the source node as a secure network coding. We prove that it is strongly secure in the sense of Harada and Yamamoto and universal secure in the sense of Silva and Kschischang, while allowing…
This paper considers a multi-source multi-relay network, in which relay nodes employ a coding scheme based on random linear network coding on source packets and generate coded packets. If a destination node collects enough coded packets, it…
We propose a simple yet effective wireless network coding and decoding technique for a multiple unicast network. It utilizes spatial diversity through cooperation between nodes which carry out distributed encoding operations dictated by…
A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation…
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic geometry codes, the algorithm is a reformulation of the…
Under the emerging network coding paradigm, intermediate nodes in the network are allowed not only to store and forward packets but also to process and mix different data flows. We propose a low-complexity cryptographic scheme that exploits…
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…
In this paper we devise a rational curve fitting algorithm and apply it to the list decoding of Reed-Solomon and BCH codes. The proposed list decoding algorithms exhibit the following significant properties. 1 The algorithm corrects up to…
Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to…
We study the problem of achieving strong secrecy over wiretap channels at negligible cost, in the sense of maintaining the overall communication rate of the same channel without secrecy constraints. Specifically, we propose and analyze two…
Lifted Reed-Solomon and multiplicity codes are classes of codes, constructed from specific sets of $m$-variate polynomials. These codes allow for the design of high-rate codes that can recover every codeword or information symbol from many…
We consider the problem of reliable communication over a network containing a hidden {\it myopic} adversary who can eavesdrop on some $z_{ro}$ links, jam some $z_{wo}$ links, and do both on some $z_{rw}$ links. We provide the first…