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Linearity and solvability in multicast networks

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3 Author(s)
Dougherty, R. ; Center for Commun. Res., San Diego, CA, USA ; Freiling, C. ; Zeger, K.

It is known that for every solvable multicast network, there exists a large enough finite-field alphabet such that a scalar linear solution exists. We prove: i) every binary solvable multicast network with at most two messages has a binary scalar linear solution; ii) for more than two messages, not every binary solvable multicast network has a binary scalar linear solution; iii) a multicast network that has a solution for a given alphabet might not have a solution for all larger alphabets.

Published in:

Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 10 )