Network security protocols depend mainly on developing cryptographic schemes and using biometric methods. These have led to several security protocols that are unbreakable based on difficulty of solving untractable mathematical problems such as factoring large integers. In this paper, Securing Networks by Employing Encoding and Decoding (SNEED) is developed to mitigate single and multiple link attacks. Network coding and shared capacity among the working paths are used to provide data protection and data integrity against network attackers and eavesdroppers. It is shown that SNEED can be implemented easily where there are k link disjoint paths between two core nodes (routers or switches) in an enterprise network. Finally, SNEED can be incorporated into various applications such as on-demand TV, satellite communications, and multimedia security.

There have been several approaches to provisioning traffic between core network nodes in Internet Service Provider networks. Such approaches aim to minimize network delay, increase capacity, and enhance security services. MATE (Multipath Adaptive Traffic Engineering) has been proposed for multipath adaptive traffic engineering between an ingress node (source) and an egress node (destination). Its novel idea is to avoid network congestion and attacks that might exist in edge and node disjoint paths between two core network nodes. This paper builds an adaptive, robust, and reliable traffic engineering scheme for better performance and operation of communication networks. This will also provision quality of service (QoS) and protection of traffic engineering to maximize network efficiency. Specifically, we present a new approach, S-MATE (secure MATE) is developed to protect the network traffic between two core nodes (routers, switches, etc.) in a cloud network. S-MATE secures against a single link attack/failure by adding redundancy in one of the operational paths between the sender and receiver. The proposed scheme can be built to secure core networks such as optical and IP networks.

We consider large-scale wireless sensor networks with n nodes, out of which k are in possession, (e.g., have sensed or collected in some other way) k information packets. In the scenarios in which network nodes are vulnerable because of, for example, limited energy or a hostile environment, it is desirable to disseminate the acquired information throughout the network so that each of the n nodes stores one (possibly coded) packet so that the original k source packets can be recovered, locally and in a computationally simple way from any k(1 + ¿) nodes for some small ¿ > 0. We develop decentralized Fountain codes based algorithms to solve this problem. Unlike all previously developed schemes, our algorithms are truly distributed, that is, nodes do not know n, k or connectivity in the network, except in their own neighborhoods, and they do not maintain any routing tables.

With the enormous increase in the usage of communication networks, protection against node and link failures became essential in the deployment of reliable networks. To manage loss of data due to node failures, we design a network protection strategy that aims to withstand such failures. In this paper we propose a protection strategy against any single node failure in the network. We deploy network coding and reduced capacity in this strategy without adding extra working paths to the readily available connection paths. The strategy is based on representing node failures by the failure of multiple links, and hence is transformed into a protection against multiple link failures. Consequently, the protection strategies proposed in, can also be applied for protection against node failures. In addition, we demonstrate the implementation aspects of the premeditated protection strategies.

In this paper we propose distributed storage algorithms for large-scale wireless sensor networks. Assume a wireless sensor network with n nodes that have limited power, memory, and bandwidth. Each node is capable of both sensing and storing data. Such sensor nodes might disappear from the network due to failures or battery depletion. Hence it is desired to design efficient schemes to collect data from these n nodes. We propose two distributed storage algorithms (DSA's) that utilize network flooding to solve this problem. In the first algorithm, DSA-I, we assume that the total number of sensors is known to each sensor in the network. We show that this algorithm is efficient in terms of the encoding and decoding operations. Furthermore, every node utilizes network flooding to disseminate its data throughout the network using a mixing time of approximately O(n). In the second algorithm, DSA-II, we assume that the total number of nodes is not known to every sensor; hence dissemination of the data does not depend on n. The encoding operations in this case take O(C mu2), where mu is the mean degree of the network graph and C is a system parameter. We evaluate the performance of the proposed algorithms through analysis and simulation. We show that the performance of the proposed algorithms matches the derived theoretical results.

Low-density parity check (LDPC) codes are a significant class of classical codes with many applications. Several good LDPC codes have been constructed using random, algebraic, and finite geometries approaches, with containing cycles of length at least six in their Tanner graphs. However, it is impossible to design a self-orthogonal parity check matrix of an LDPC code without introducing cycles of length four. In this paper, a new class of quantum LDPC codes based on lines and points of finite geometries is constructed. The parity check matrices of these codes are adapted to be self- orthogonal with containing only one cycle of length four in each pair of two rows. Also, the column and row weights, and bounds on the minimum distance of these codes are given. As a consequence, these codes can be encoded using shift-register encoding algorithms and can be decoded using iterative decoding algorithms over various quantum depolarizing channels.

Protecting against link failures in communication networks is essential to increase robustness, accessibility, and reliability of data transmission. Recently, network coding has been proposed as a solution to provide agile and cost efficient network protection against link failures, which does not require data rerouting, or packet retransmission. To achieve this, separate paths have to be provisioned to carry encoded packets, hence requiring either the addition of extra links, or reserving some of the resources for this purpose. In this paper, we propose network protection codes against a single link failure using network coding, where a separate path using reserved links is not needed. In this case portions of the link capacities are used to carry the encoded packets. The scheme is extended to protect against multiple link failures and can be implemented at an overlay layer. Although this leads to reducing the network capacity, the network capacity reduction is asymptotically small in most cases of practical interest. We demonstrate that such network protection codes are equivalent to error correcting codes for erasure channels. Finally, we study the encoding and decoding operations of such codes over the binary field.

We consider large-scale networks with n nodes, out of which k are in possession, (e.g., have sensed or collected in some other way) k information packets. In the scenarios in which network nodes are vulnerable because of, for example, limited energy or a hostile environment, it is desirable to disseminate the acquired information throughout the network so that each of the n nodes stores one (possibly coded) packet and the original k source packets can be recovered later in a computationally simple way from any (1 + isin)k nodes for some small isin > 0. We developed two distributed algorithms for solving this problem based on simple random walks and Fountain codes. Unlike all previously developed schemes, our solution is truly distributed, that is, nodes do not know n, k or connectivity in the network, except in their own neighborhoods, and they do not maintain any routing tables. In the first algorithm, all the sensors have the knowledge of n and k. In the second algorithm, each sensor estimates these parameters through the random walk dissemination. We present analysis of the communication/transmission and encoding/decoding complexity of these two algorithms, and provide extensive simulation results as well.

Subsystem codes are the most versatile class of quantum error-correcting codes known to date that combine the best features of all known passive and active error-control schemes. The subsystem code is a subspace of the quantum state space that is decomposed into a tensor product of two vector spaces: the subsystem and the co-subsystem. A generic method to derive subsystem codes from existing subsystem codes is given that allows one to trade the dimensions of subsystem and co-subsystem while maintaining or improving the minimum distance. As a consequence, it is shown that all pure MDS subsystem codes are derived from MDS stabilizer codes. The existence of numerous families of MDS subsystem codes is established. Propagation rules are derived that allow one to obtain longer and shorter subsystem codes from given subsystem codes. Furthermore, propagation rules are derived that allow one to construct a new subsystem code by combining two given subsystem codes.

We consider a distributed storage problem in a large-scale wireless sensor network with n nodes among which k acquire (sense) independent data. The goal is to disseminate the acquired information throughout the network so that each of the n sensors stores one possibly coded packet and the original k data packets can be recovered later in a computationally simple way from any (1 + ∈)k of nodes for some small ∈ ≫ 0. We propose two Raptor codes based distributed storage algorithms for solving this problem. In the first algorithm, all the sensors have the knowledge of n and k. In the second one, we assume that no sensor has such global information.

Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit constructions. A quantum Singleton bound for pure convolutional stabilizer codes is given. A familiy of quantum convolutional codes is derived from generalized Reed-Solomon codes. These codes are shown to be optimal with respect to the (quantum) Singleton bound.

Duadic group algebra codes are a generalization of quadratic residue codes. This paper addresses an open problem raised by Zhu concerning the existence of duadic group algebra codes. These codes can be used to construct degenerate quantum stabilizer codes that have the nice feature that many errors of small weight do not need error correction.

Classical Bose–Chaudhuri–Hocquenghem (BCH) codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length$n$can contain its dual code only if its designed distance$\delta =O(\sqrt {n})$, and the converse is proved in the case of narrow-sense codes. Furthermore, the dimension of narrow-sense BCH codes with small design distance is completely determined, and – consequently – the bounds on their minimum distance are improved. These results make it possible to determine the parameters of quantum BCH codes in terms of their design parameters.

Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is -unfortunately- itself prone to errors. In this paper, examples of degenerate quantum codes are constructed that alleviate this problem in that they allow some errors of small weight that do not require active error correction. In particular, two new families of [[n, 1, ges radicn]]qdegenerate quantum codes are derived from classical duadic codes

An attractive feature of BCH codes is that one can infer valuable information from their design parameters (length, size of the finite field, and designed distance), such as bounds on the minimum distance and dimension of the code. In this paper, it is shown that one can also deduce from the design parameters whether or not a primitive, narrow-sense BCH contains its Euclidean or Hermitian dual code. This information is invaluable in the construction of quantum BCH codes. A new proof is provided for the dimension of BCH codes with small designed distance, and simple bounds on the minimum distance of such codes and their duals are derived as a consequence. These results allow us to derive the parameters of two families of primitive quantum BCH codes as a function of their design parameters