In this letter, we provide a method for deriving the first exact expression for the decoding success probability of sparse random linear network coding over erasure channels. The key idea of the proposed method is to ...
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In this letter, we provide a method for deriving the first exact expression for the decoding success probability of sparse random linear network coding over erasure channels. The key idea of the proposed method is to transform the characterization of the full rank probability of a sparserandom matrix into the characterization of the homomorphism transform of the sparse distribution and to obtain a closed-form exact expression for the homomorphism transform of the sparse distribution. The former is solved by employing Mobius inversion theorem and the property of the homomorphism transform, and the latter is solved by employing the feature of the sparse distribution and the property of the nontrivial character of a finite field.
Characterization of the rank distribution of a sparserandom matrix over a finite field can be decomposed into two subproblems. The first subproblem is the characterization of the probability p(i,n) that an n-dimensio...
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Characterization of the rank distribution of a sparserandom matrix over a finite field can be decomposed into two subproblems. The first subproblem is the characterization of the probability p(i,n) that an n-dimensional vector is linearly dependent of other i linearly independent n-dimensional vectors. The second subproblem is the characterization of the rank distribution of a sparserandom matrix as a function of p(i,n). In this letter, we focus on the second subproblem and present an exact solution to it. The derivation is based on an absorbing Markov chain and the eigen decomposition of the transition matrix. Compared with the state-of-the-art expressions, the derived expression is closed-form and of lower complexity. As a necessity for the exactness of the derived expression, we prove that the derived expression is equivalent to the state-of-the-art expressions.
sparse random linear network coding (SRLNC) is a promising solution for reducing the complexity of randomlinearnetworkcoding (RLNC). RLNC can be modeled as a linear operator channel (LOC). It is well known that the...
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sparse random linear network coding (SRLNC) is a promising solution for reducing the complexity of randomlinearnetworkcoding (RLNC). RLNC can be modeled as a linear operator channel (LOC). It is well known that the normalized channel capacity of LOC is characterized by the rank distribution of the transfer matrix. In this paper, we study the rank distribution of SRLNC. By exploiting the definition of linear dependence of the vectors, we first derive a novel approximation to the probability of a sparserandom matrix being non-full rank. By using the Gauss coefficient, we then provide a closed approximation to the rank distribution of a sparserandom matrix over a finite field. The simulation and numerical results show that our proposed approximation to the rank distribution of sparse matrices is very tight and outperforms the state-of-the-art results, except for the finite field size and the number of input packets are small, and the sparsity of the matrices is large.
randomlinearnetworkcoding 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. sparsenetworkcoding ...
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randomlinearnetworkcoding 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. sparsenetworkcoding (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.
Security issue occupies an important part in all communication system and especially for new generation networks. Among these networks, we find Delay Tolerant Mobile networks (DTMNs) which are a class of useful but ch...
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ISBN:
(纸本)9781467380966
Security issue occupies an important part in all communication system and especially for new generation networks. Among these networks, we find Delay Tolerant Mobile networks (DTMNs) which are a class of useful but challenging networks. Combining networkcoding (NC) and clustering for routing in such networks gives more efficiency and copes with routing reliability problem among large scale networks. Our work's concern is to build a secure networkcoding scheme in the presence of eavesdroppers in large-scale DTMNs. Therefore, we used a cluster based routing protocol dedicated to DTMN specificities. In addition, we used sparse random linear network coding (SRLNC) to feat low computational capabilities requirement in such networks. Furthermore, we addressed the packets retransmission decision problem for SRLNC with a fair trade-off throughput/overhead. The results are very encouraging and the proposed routing scheme has the advantage to be reliable as well as secure for large scale DTMN.
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