2013/01/14 by Vijayvaradharaj T. Muralidharan, Muralidharan, Vijayvaradharaj T., B. Sundar Rajan +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced MIMO Systems Optimization #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Full-Duplex Wireless Communications #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1301.3003
11 pages, 7 figures
arxiv created 2013/01/14 · openalex publication_date 2013/01/14 · arxiv updated 2013/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the vector linear solvability of networks over a field \mathbbFq. It is well known that a scalar linear solution over \mathbbFq exists for a network if and only if the network is matroidal with respect to a matroid representable over \mathbbFq. A discrete polymatroid is the multi-set analogue of a matroid. In this paper, a discrete polymatroidal network is defined and it is shown that a vector linear solution over a field \mathbbFq exists for a network if and only if the network is discrete polymatroidal with respect to a discrete polymatroid representable over \mathbbFq. An algorithm to construct networks starting from a discrete polymatroid is provided. Every representation over \mathbbFq for the discrete polymatroid, results in a vector linear solution over \mathbbFq for the constructed network. Examples which illustrate the construction algorithm are provided, in which the resulting networks admit vector linear solution but no scalar linear solution over \mathbbFq.