Grassmannian codes are known to be useful in error correction for random network coding. Recently, they were used to prove that vector network codes outperform scalar linear network codes, on multicast networks, with ...
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Grassmannian codes are known to be useful in error correction for random network coding. Recently, they were used to prove that vector network codes outperform scalar linear network codes, on multicast networks, with respect to the alphabet size. The multicast networks which were used for this purpose are generalized combination networks. In both the scalar and the vector network coding solutions, the subspace distance is used as the distance measure for the codes which solve the network coding problem in the generalized combination networks. In this paper, we show that the subspace distance can be replaced with two other possible distance measures which generalize the subspace distance. These two distance measures are shown to be equivalent under an orthogonal transformation. It is proved that the Grassmannian codes with the new distance measures generalize the Grassmannian codes with the subspace distance and the subspace designs with the strength of the design. Furthermore, optimal Grassmannian codes with the new distance measures have minimal requirements for the network coding solutions of some generalized combination networks. The coding problems related to these two distance measures, especially with respect to network coding, are discussed. Finally, by using these new concepts, it is proved that the codes in the Hamming scheme form a subfamily of the Grassmannian codes.
network coding simplifies routing decisions, improves throughput, and increases tolerance against packet loss. A fundamental limitation, however, is delay: decoding requires as many independent linear combinations as ...
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network coding simplifies routing decisions, improves throughput, and increases tolerance against packet loss. A fundamental limitation, however, is delay: decoding requires as many independent linear combinations as data blocks. Prioritized network coding reduces this delay problem by introducing a hierarchy of prioritization layers. What remains is the problem of choosing a layer to approach two often-contradicting goals: reduce delay until prioritized layers can be decoded and keep the total number of transmissions low. In this paper, we propose an algorithm for this problem that - based on limited feedback - primarily minimizes per-layer delay but identifies opportunities to reduce the required transmissions when per-layer delay is unaffected. Our evaluation shows that our algorithm improves per-layer delay compared to hierarchical network coding and is close to the theoretical optimum number of total transmissions. Moreover, we demonstrate how the proposed algorithm can benefit smart-factory applications that operationalize delay-sensitive information from the production process.
Combining topology control with network coding has been recently noticed which provides essential advantages, such as lower energy consumption and higher lifetime. In this letter, we utilize optimization and graph the...
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Combining topology control with network coding has been recently noticed which provides essential advantages, such as lower energy consumption and higher lifetime. In this letter, we utilize optimization and graph theory to propose a mathematical perspective for combining network coding with transmission range adjustment in wireless sensor network (WSN). For this aim, we define an extended optimization problem based on two vectors of variables, including transmission range and network flow. In particular, it is proved that there is a coding solution if and only if the extended optimization problem has at least an optimal solution. Due to this theorem, a new objective function is provided which is more practical to prolong the lifetime of WSNs. Simulation results demonstrate that the proposed model could adjust transmission range efficiently to obtain the optimal lifetime for network-coding-based WSNs.
We study network coding gaps for the problem of makespan minimization of multiple unicasts. In this problem distinct packets at different nodes in a network need to be delivered to a destination specific to each packe...
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ISBN:
(数字)9781728196213
ISBN:
(纸本)9781728196220
We study network coding gaps for the problem of makespan minimization of multiple unicasts. In this problem distinct packets at different nodes in a network need to be delivered to a destination specific to each packet, as fast as possible. The network coding gap specifies how much coding packets together in a network can help compared to the more natural approach of routing. While makespan minimization using routing has been intensely studied for the multiple unicasts problem, no bounds on network coding gaps for this problem are known. We develop new techniques which allow us to upper bound the network coding gap for the makespan of k unicasts, proving this gap is at most polylogarithmic in k. Complementing this result, we show there exist instances of k unicasts for which this coding gap is polylogarithmic in k. Our results also hold for average completion time, and more generally any lp norm of completion times.
Random linear network coding is a promising coding scheme to increase the robustness and reliability of network systems. However, one of its major drawbacks is the high computational complexity. Sparse network coding ...
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Random linear network coding is a promising coding scheme to increase the robustness and reliability of network systems. However, one of its major drawbacks is the high computational complexity. Sparse network coding (SNC) was proposed to reduce the computational complexity at the expense of larger communication overhead. However, the performance evaluation of SNC is still a major research topic due to an inaccurate expression for the behavior of sparse matrices. In this letter, we present two approximation models to analyze the probability distribution of the rank of sparse matrices. We use our models to derive the average number of required transmissions in the SNC scheme. Our results show that the proposed models predict the rank of sparse matrices and the average number of transmissions with a maximum deviation of 4% and 6%, respectively.
network coding has received great attention for its ability to dramatically improve the performance of wireless networks. However, there still is a lack of research on how and to which degree the packet size affects t...
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network coding has received great attention for its ability to dramatically improve the performance of wireless networks. However, there still is a lack of research on how and to which degree the packet size affects the performance of a wireless network with network coding. In this letter, we study the issue of optimal packet size for inter-flow network coding enabled two-hop error-prone wireless networks with the IEEE 802.11. We analyze the network throughput of such networks and then derive the optimal packet size for maximizing the network throughput under various cases. The simulation results validate the accuracy of our analytical results.
From the paper, we propose a method of relay selection for underwater acoustic cooperative communication which adopted network coding. On the basis of choosing the relay node, we also designed a power distribution mea...
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ISBN:
(数字)9781728172361
ISBN:
(纸本)9781728172378
From the paper, we propose a method of relay selection for underwater acoustic cooperative communication which adopted network coding. On the basis of choosing the relay node, we also designed a power distribution measure. The relay selection scheme takes transmission delay and channel gain as the selection indicators, and the high-performance relay transmission nodes are selected through the standardized joint evaluation of the two indicators. When we select the most suitable transmission node for sending the information, this paper uses the proposed underwater acoustic network and introduces network coding technology to design a power distribution method. Since the node that transmits and forwards information processes more messages than the node which sends information, the relay node needs more power to ensure correct transmission. After calculation and simulation verification, this paper finds the power allocation ratio to ensure information transmission. In addition, through simulation verification, the communication performance of the optimized power allocation proposed is better than the traditional power parity solution when the symbol error rate is same.
We consider a network where two nodes are mutually exchanging information. The intermediate nodes are assumed to employ linear network coding. For this setting, network coding security, which was originally considered...
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A novel implementation of a special class of Galois ring, in which the multiplication can be realized by a cyclic convolution, is applied to the construction of network codes. The primitive operations involved are byt...
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We propose a novel hybrid universal network-coding cryptosystem (HUNCC) to obtain secure post-quantum cryptography at high communication rates. The secure network-coding scheme we offer is hybrid in the sense that it ...
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We propose a novel hybrid universal network-coding cryptosystem (HUNCC) to obtain secure post-quantum cryptography at high communication rates. The secure network-coding scheme we offer is hybrid in the sense that it combines information-theory security with public-key cryptography. In addition, the scheme is general and can be applied to any communication network, and to any public-key cryptosystem. Our hybrid scheme is based on the information theoretic notion of individual secrecy, which traditionally relies on the assumption that an eavesdropper can only observe a subset of the communication links between the trusted parties – an assumption that is often challenging to enforce. For this setting, several code constructions have been developed, where the messages are linearly mixed before transmission over each of the paths in a way that guarantees that an adversary which observes only a subset has sufficient uncertainty about each individual message. Instead, in this paper, we take a computational viewpoint, and construct a coding scheme in which an arbitrary secure cryptosystem is utilized on a subset of the links, while a pre-processing similar to the one in individual security is utilized. Under this scheme, we demonstrate 1) a computational security guarantee for an adversary which observes the entirety of the links 2) an information theoretic security guarantee for an adversary which observes a subset of the links, and 3) information rates which approach the capacity of the network and greatly improve upon the current solutions. A perhaps surprising consequence of our scheme is that, to guarantee a computational security level b, it is sufficient to encrypt a single link using a computational post-quantum scheme. That is, using HUNCC, we can ensure post-quantum security in networks where it is not possible to use public-key encryption over all the links in the network. In addition, the information rate approaches 1 as the number of communication links increa
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