Application Of Network Coding Research Articles

Lifted MDS Codes over Finite Fields

MDS codes are elegant constructions in coding theory and have mode important applications in network coding, distributed data storage, communication systems etc. In this study, a method is given which MDS codes are lifted to a higher finite field. The presented method satisfies the protection of the distance and creating the MDS code over the $F_q$ by using MDS code over $F_p.$

On Security Against Pollution Attacks in Network Coding Enabled 5G Networks

Future communication networks need to harness the available spectrum more efficiently to cater the requirements of the ever-increasing digital devices. Higher data rate with low latency is a major requirement of future communication networks. Network coding is arising once more as an enabler for satisfying the bandwidth requirements of future multimedia and resource hungry services. However, network coding techniques suffer from security vulnerabilities that will eliminate any bandwidth profits. Specific attacks in network coding like pollution attacks are extremely dangerous due to the nature of encoding and spreading inside the whole network. They deteriorate the bandwidth efficiency and even disrupt proper decoding of any message at the receiving end. Further, in a wireless environment, the authenticity of intermediate nodes is not easy to ensure, making it easier for an attacker to be part of the network. Thus counteracting pollution attacks in network coding becomes very important for practical applications of network coding enabled networks in the future generations of mobile communication. There has been a lot of research interest in this direction resulting in a few interesting approaches for secure network coding. However, most of the schemes fail to meet the expected standards or incur high overheads to the system. Schemes addressing the dense heterogeneous networks efficiently are yet to be proposed. This study surveys the security vulnerabilities of network coding, particularly those imposed by pollution attacks, as well as, the corresponding countermeasures. The survey goes a step further and includes a potential secure implementation of network coding enabled 5G networks, based on cooperating small cells.

New lower bounds for partial k‐parallelisms

AbstractDue to the applications in network coding, subspace codes and designs have received many attentions. Suppose that and is an ‐dimensional space over the finite field . A ‐spread is a ‐set of ‐dimensional subspaces of such that each nonzero vector is contained in exactly one element of it. A partial ‐parallelism in is a set of pairwise disjoint ‐spreads. As the number of ‐dimensional subspaces in is , there are at most spreads in a partial ‐parallelism. By studying the independence numbers of Cayley graphs associated to a special type of partial ‐parallelisms in , we obtain new lower bounds for partial ‐parallelisms. In particular, we show that there exist at least pairwise disjoint ‐spreads in .

Network Coding For Data Delivery in Caching at Edge: Concept, Model, and Algorithms

To deal with the explosive traffic demand, caching at the edge of mobile networks has been proposed to improve the quality of user experience. Presently, the edge caching systems are based on the direct and simple relay transmission, which is hard to achieve high system throughput and good content service. In such situations, network coding can effectively solve these problems. One problem arises in the application of network coding: how to form ‘X’ topology network. We formulate the ‘X’ topology formation problem as a function of system throughput and content service satisfaction degree. Then we propose a coalition game theory based algorithm to solve this NP-hard problem and prove the Nash stability of our coalition formation game. We evaluate our proposed algorithm through extensive simulations in different network environments. The experiment results demonstrate that our algorithm achieves nearly optimal performance and significantly outperforms the four widely-accepted baseline algorithms.

EdDSA Over Galois Field GF(p^m) for Multimedia Data

The Edwards-curve Digital Signature Algorithm (EdDSA) was proposed to perform fast public-key digital signatures and thus replace the Elliptic-Curve Digital Signature Algorithm. Its key advantages over the latter include higher performance and straightforward, secure implementation for embedded devices. EdDSA algorithm is implemented over Galois Field. The operations like addition and multiplication in Galois field are different compared to normal addition and multiplication. Hence implementing EdDSA over Galois field provides more security compared to the conventional EdDSA signature. The basics of Galois Field and its application to store data is introduced. The finite field GF (pm) is an indispensable mathematical tool for some research fields such as information coding, cryptology, theory and application of network coding.

Performance analysis of multiple access relay channels for non-coherent modulations

One of the most important applications of network coding is the Multiple Access Relay Channel (MARC) technique in which source terminals transmit independent data blocks over one or more relay terminals to a common destination terminal. In recent years, MARC has become one of the vital network coding applications in the area of innovative wireless cooperative communications for enhancing spectral efficiency. In this paper, non-coherent binary frequency shift keying (BFSK) modulation and differential binary phase shift keying (DPSK) modulation techniques are applied to the decode-and-forward (DF)-based MARC model and the average bit error rate (BER) of the proposed system is derived theoretically by using the maximum likelihood (ML) decision rule. The simulation results show that the BER performance of DPSK modulation is better than the non-coherent BFSK and full diversity gain is achieved in both modulation techniques. We also propose a power allocation scheme for the proposed system model which optimizes the power allocated to the source and relay transmissions. Depending on the location of the relay, performance gains up to 1.25 dB are achieved with the proposed optimum power allocation (OPA) scheme. Also, the mathematical derivations are verified through Monte-Carlo simulations and the superior performance of the OPA over equal power allocation (EPA) is observed.

A Policy-Aware Enforcement Logic for Appropriately Invoking Network Coding

Network coding has been shown to offer significant throughput benefits over certain wireless network topologies. However, the application of network coding may not always improve the network performance. In this paper, we first provide an analytical study, which helps in assessing when network coding is preferable to a traditional store-and-forward approach. Interestingly, our study reveals that in many topological scenarios, network coding can in fact hurt the throughput performance; in such scenarios, applying the store-and-forward approach leads to higher network throughput. We validate our analytical findings via extensive testbed experiments. Guided by our findings as our primary contribution, we design and implement PACE, a Policy-Aware Coding Enforcement logic that enables network coding only when it is expected to offer performance benefits. Specifically, PACE leverages a minimal set of periodic link quality measurements in order to make per-flow online decisions with regards to when network coding should be activated, and when store-and-forward is preferable. It can be easily embedded into network-coding-aware routers as a user-level or kernel-level software utility. We evaluate the efficacy of PACE via: 1) ns-3 simulations, and 2) experiments on a wireless testbed. We observe that our scheme wisely activates network coding only when appropriate, thereby improving the total network throughput by as much as 350% in some scenarios.

네트워크 코딩을 쓰는 언더레이 인지 무선 네트워크에서의 주파수 할당과 경로 선택 기법

In this paper, we propose frequency allocation and path selection scheme in underlay cognitive radio (CR) networks using network coding. In the proposed scheme, we choose the path with consideration of network coding and interference temperature in underlay CR networks and propose an optimization problem to maximize the system throughput of secondary users (SUs). Then, we represent the proposed optimization problem as the multi-dimensional multiple-choice knapsack problem and give the theoretical upper bound for the system throughput of SUs by using linear programming. Finally, we compute the system throughput of SUs by using brute-force search (BFS) and link quality first (LQF) scheme in underlay CR networks. Simulation results show that the system throughput of SUs with BFS is higher than that with LQF in underlay CR networks with and without application of network coding, respectively.

An enumeration of the equivalence classes of self-dual matrix codes

As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes, space-time codes over finite fields, and array codes. We focus on characterizing matrix codes that are both efficient (have high rate) and effective at error correction (have high minimum rank-distance). It is well known that the inherent trade-off between dimension and minimum distance for a matrix code is reversed for its dual code; specifically, if a matrix code has high dimension and low minimum distance, then its dual code will have low dimension and high minimum distance. With an aim towards finding codes with a perfectly balanced trade-off, we study self-dual matrix codes. In this work, we develop a framework based on double cosets of the matrix-equivalence maps to provide a complete classification of the equivalence classes of self-dual matrix codes, and we employ this method to enumerate the equivalence classes of these codes for small parameters.

Compressive Soft Forwarding in Network-Coded Multiple-Access Relay Channels

In this paper, we design a novel estimate-and-forward (EF) protocol in multiple-access relay channels (MARCs) where two correlated sources transmit their information to the common destination with the help of a relay. With the application of network coding (NC) at the relay, the network-coded soft symbols contain redundant information due to the correlated sources, which can be compressed before being forwarded. Specifically, we first derive the value of the network-coded soft symbol by considering the correlation of the two sources. Due to this correlation, the majority of soft symbol values are close to one. Then, we convert network-coded soft symbol vector into a sparse vector, which is suitable for compression by using the compressive sensing (CS). Next, we analyze the performance of the proposed EF protocol by comparing the soft symbol value and received signal-to-noise ratio (SNR) with the conventional EF protocol. Simulations show that our protocol can achieve the same bit error rate (BER) as the conventional EF protocol with proper compression rates, and it consumes much less transmission time due to the compression.

Content distribution in VANETs

Advances in vehicular communications technology are making content distribution to vehicles more effective and increasingly more popular. This paper presents state of the art technologies and protocols for content distribution in VANETs. Major challenges are Internet access spectrum scarcity, mobility, connectivity intermittence and scalability. Aspects covered in this paper include: coexistence of WiFi and LTE; application of network coding; protection from pollution attacks; incentive design for cooperation enforcement; QoS support for video streaming applications. Simulation and testbed results are presented to support the findings. Critical issues that will determine future directions in this area are identified and discussed.

Gray Codes and Enumerative Coding for Vector Spaces

Gray codes for vector spaces are considered in two graphs: the Grassmann graph, and the projective-space graph, both of which have recently found applications in network coding. For the Grassmann graph, constructions of cyclic optimal codes are given for all parameters. As for the projective-space graph, two constructions for specific parameters are provided, as well some nonexistence results. Furthermore, encoding and decoding algorithms are given for the Grassmannian Gray code, which induce an enumerative-coding scheme. The computational complexity of the algorithms is at least as low as known schemes, and for certain parameter ranges, the new scheme outperforms previously known ones.

The Improvement of End to End Delays in Network Management System using Network coding

In this paper, we consider the application of network coding(NC) for network management system of Radio and Television Broadcasting Stations in wireless network using a narrow band radios modem &Routers ) as a means of transmission to communicate between the loins broadcast TV/FM stations . Our main contribution is the application of NCimproved by the proposed an effective strategy,called Fast Forwarding Strategy (FFS) compared to a classical routing strategy with a level of providing guarantees of service quality (QoS) expressed in terms of reducing the End-to-End Delays (EED) from source to destination.The practical and theoretical study, carried out by the authors, show that the EED of proposed strategy outperforms that of the classical strategy.

The Application of Network Coding in Asymmetric Cooperative Diversity Communication

该文提出了网络编码在非对称三点协作传输系统中的应用。通过协作分集技术和网络编码技术的联合运用，不但可得到无线通信传输系统的分集增益，也可得到系统的编码增益。该文设计的方案，充分考虑无线通信环境的差异性，利用非对称调制方式，在保证较差通信环境中取得通信可靠性的同时，在较优链路采取较高速率进行传输，利用较优链路传输更多的信息，实现系统资源的充分利用。在方案的具体实现中，通过在中继链路的中继节点加入已知信息实现网络编码，使得系统的译码性能得到增加。仿真结果表明，将网络编码技术应用于非对称协作分集通信中，相对比非协作传输方案可增加分集增益，降低系统的误比特率。跟传统对称传输系统相比，可充分利用系统资源，提升了系统传输容量。

On the Security and Efficiency of Content Distribution via Network Coding

Content distribution via network coding has received a lot of attention lately. However, direct application of network coding may be insecure. In particular, attackers can inject bogus” data to corrupt the content distribution process so as to hinder the information dispersal or even deplete the network resource. Therefore, content verification is an important and practical issue when network coding is employed. When random linear network coding is used, it is infeasible for the source of the content to sign all the data, and hence, the traditional hash-and-sign” methods are no longer applicable. Recently, a new on-the-fly verification technique has been proposed by Krohn et al. (IEEE S&P '04), which employs a classical homomorphic hash function. However, this technique is difficult to be applied to network coding because of high computational and communication overhead. We explore this issue further by carefully analyzing different types of overhead, and propose methods to help reducing both the computational and communication cost, and provide provable security at the same time.

Large constant dimension codes and lexicodes

Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of $\mathbb F$qn with a given dimension. A computer search for large constant dimension codes is usually inefficient since the search space domain is extremely large. Even so, we found that some constant dimension lexicodes are larger than other known codes. We show how to make the computer search more efficient. In this context we present a formula for the computation of the distance between two subspaces, not necessarily of the same dimension.

Application of Network Coding in Rateless Transmission over Wireless Relay Networks

In this paper, a novel transmission scheme which incorporates network coding into rateless transmission over relay networks is proposed. This technique allows partial information about the upcoming message block to be transmitted during the current block transmission, hence reducing the required number of transmissions and improving the spectral efficiency. Different techniques for applying network coding to several fading models are discussed, and their relationships to an erasure channel model is explained. An optimisation of the network coding weight is given, and we show that by choosing the weight that minimizes the duration of the current block transmission and sending sufficient information about subsequent block, we can improve the overall performance.

Survey of Network Coding and Its Applications

SUMMARY This survey summarizes the state-of-the-art research on network coding, mainly focusing on its applications to computer networking. Network coding generalizes traditional store-and-forward routing techniques by allowing intermediate nodes in networks to encode several received packets into a single coded packet before forwarding. Network coding was proposed in 2000, and since then, it has been studied extensively in the field of computer networking. In this survey, we first summarize linear network coding and provide a taxonomy of network coding research, i.e., the network coding design problem and network coding applications. Moreover, the latter is subdivided into throughput/capacity enhancement, robustness enhancement, network tomography, and security. We then discuss the fundamental characteristics of network coding and diverse applications of network coding in details, following the above taxonomy.

Secure Network Coding in DTNs

The application of network coding can significantly improve the performance of message delivery in delay tolerant networks, assuming all participants behave honestly. However, if some nodes of the network are compromised, the adversary can launch pollution attack and this way can destroy large amount of data with small effort. Current solutions against pollution attack require public key infrastructure, that is often not available in mobile ad-hoc networks. Our proposal allows packets to verify each other, hence an intermediate node can decide whether these packets can be encoded together without authenticating the source.

Enumerative Coding for Grassmannian Space

The Grassmannian space Gq(n, k) is the set of all k-dimensional subspaces of the vector space Fqn. Recently, codes in the Grassmannian have found an application in network coding. The main goal of this paper is to present efficient enumerative encoding and decoding techniques for the Grassmannian. These coding techniques are based on two different orders for the Grassmannian induced by different representations of k-dimensional subspaces of Fqn. One enumerative coding method is based on a Ferrers diagram representation and on an order for Gq(n, k) based on this representation. The complexity of this enumerative coding is O(k5/2(n - k)5/2) digit operations. Another order of the Grassmannian is based on a combination of an identifying vector and a reduced row echelon form representation of subspaces. The complexity of the enumerative coding, based on this order, is O(nk(n - k) log n log log n) digit operations. A combination of the two methods reduces the complexity on average by a constant factor.