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In this paper, we present a practical algorithm to construct the convolutional multicast network coding over any finite directed cyclic network. The dual line graph of a directed cyclic graph is considered as a system. By regarding the global encoding kernels in the original graph as the corresponding inputs or outputs of some subsystem and the local encoding kernels in original graph as gains of...
A wiretap network with errors occurred on some edges is called a erroneous wiretap networks, for which we propose a nested code approach. Given a linear network code for an erroneous wiretap network, we derive the necessary and sufficient condition for a nested code to combat errors on d edges and prevent eavesdropping from μ edges. Furthermore, we prove that using nested codes the maximum rate at...
Note that network coding allows immediate nodes to mix information from different data flows. On the basis of this observation, we prove that under suitable conditions, communicators can communicate with perfect secrecy over wiretap networks. Our method of secure communication over wiretap networks without keys is fundamentally distinct from cryptographic means. Furthermore, a linear network code...
Capacity of network coding in cyclic networks can be strictly better than routing. Harvey et al. showed that it exists in the practical scenarios such as the widespread P2P networks. Thus, it is of application significance to investigate how to construct network code in cyclic networks. According to Li et al., there are four levels of network code in cyclic networks, including convolutional multicast...
Network coding in cyclic networks may have better performance than network coding in acyclic networks with regard to the multi-unicast scenarios. Harvey et al. showed that network coding in cyclic networks can be strictly better than fractional routing in conservative networks which have widely practical scenarios such as P2P networks. Hence, we motivated investigating how to achieve that better performance...
Motivated by the elegant relationships of the row vectors of the Jacket matrix Jn and its inverse matrix Jn-1, which are both consisted of Fibonacci number sequence over the finite field GF(p), a novel network work code is constructed structurally with efficiency. The present network codes have advantages of eavesdropper-preventing and error-detecting ability, which are decided by the properly selected...
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