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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 them with L × L coding matrices that play a similar role as coding coefficients in scalar coding. Our algorithms for scalar network jointly optimize...
We present a polynomial time algorithm for multicasting rate h to N receivers over deterministic networks. Our algorithm requires intermediate network nodes to perform coding operations over vectors of a finite length L, through multiplication with L × L binary coding matrices that play the same role as coding coefficients over graphs. Our code design consists in selecting these matrices so that each...
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