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Algebraic Algorithms for Vector Network Coding

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Multiscale representations such as the wavelet transform are useful for many signal processing tasks. Graphs are flexible models to represent complex networks and a spectral graph wavelet transform (SGWT) has recently been developed as a generalization of ...

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We here summarize some recent advances in the study of linear deterministic networks, recently proposed as approximations for wireless channels. This work started by extending the algebraic framework developed for multicasting over graphs in [1] to include ...

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Vector Network Coding Algorithms

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We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying th ...

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The periodic QR algorithm is a disguised QR algorithm

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The periodic QR algorithm is a strongly backward stable method for computing the eigenvalues of products of matrices, or equivalently for computing the eigenvalues of block cyclic matrices. The main purpose of this paper is to show that this algorithm is n ...

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On the Throughput Improvement due to Limited Complexity Processing at Relay Nodes

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We consider a source that transmits information to a receiver by routing it over a communication network represented by a graph and examine rate benefits that finite complexity processing at the intermediate nodes may offer. We show that there exist config ...

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