A Class of Non-Linearly Solvable Networks

Joseph Connelly; Kenneth Zeger

doi:10.1109/tit.2016.2618379

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arXiv · 1601.03803

A Class of Non-Linearly Solvable Networks

Joseph Connelly·Kenneth Zeger

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Abstract

For each integer $m \geq 2$, a network is constructed which is solvable over an alphabet of size $m$ but is not solvable over any smaller alphabets. If $m$ is composite, then the network has no vector linear solution over any $R$-module alphabet and is not asymptotically linear solvable over any finite-field alphabet. The network's capacity is shown to equal one, and when $m$ is composite, its linear capacity is shown to be bounded away from one for all finite-field alphabets.

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Joseph Connelly, Kenneth Zeger. 2016-01-15. A Class of Non-Linearly Solvable Networks. https://doi.org/10.1109/tit.2016.2618379

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