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A Homomorphism Transform Based Analysis of sparse random linear network coding Over Erasure Channels

IEEE COMMUNICATIONS LETTERS 2022年第9期26卷 2009-2013页

作者： Chen, Wenlin Lu, Fang Dong, Yan Huazhong Univ Sci & Technol Sch Elect Informat & Commun Wuhan 430074 Peoples R China

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 sparse random 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.

关键词： Decoding Transforms Additives sparse matrices Reliability Encoding Receivers sparse random linear network coding sparse matrices full rank probability

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Improved Expression for Rank Distribution of sparse random linear network coding

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IEEE COMMUNICATIONS LETTERS 2021年第5期25卷 1472-1476页

作者： Chen, Wenlin Lu, Fang Dong, Yan Huazhong Univ Sci & Technol Sch Elect Informat & Commun Wuhan 430074 Peoples R China

Characterization of the rank distribution of a sparse random 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 sparse random 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.

关键词： sparse matrices Matrix decomposition Decoding Eigenvalues and eigenfunctions Markov processes Receivers network coding sparse random linear network coding rank distribution sparse matrices

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The Rank Distribution of sparse random linear network coding

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IEEE ACCESS 2019年 7卷 43806-43819页

作者： Chen, Wenlin Lu, Fang Dong, Yan Huazhong Univ Sci & Technol Sch Elect Informat & Commun Wuhan 430074 Hubei Peoples R China

sparse random linear network coding (SRLNC) is a promising solution for reducing the complexity of random linear network coding (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 sparse random matrix being non-full rank. By using the Gauss coefficient, we then provide a closed approximation to the rank distribution of a sparse random 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.

关键词： Rank distribution sparse matrices sparse random linear network coding

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An Analytical Model for Rank Distribution in sparse network coding

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IEEE COMMUNICATIONS LETTERS 2019年第4期23卷 556-559页

作者： Sehat, Hadi Pahlevani, Peyman Inst Adv Studies Basic Sci Zanjan *** Iran

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.

关键词： sparse random linear network coding rank of sparse matrix network coding

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Secure sparse network coding for Reliable Routing in Large Scale DTMN 3

Secure Sparse Network Coding for Reliable Routing in Large S...

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3rd International Workshop on RFID and Adaptive Wireless Sensor networks (RAWSN)

作者： Chanyour, Tarik Saadane, Rachid Belkasmi, Mostafa Mohammed V Rabat Univ ENSIAS SIME Labo Rabat Morocco SIRC2S LASI EHTP Casablanca Morocco

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 network coding (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 network coding 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.

关键词： DTMN routing secure network coding sparse random linear network coding clustring large scale DTMN

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