2016/07/06 by Niladri Das, Brijesh Kumar, Das, Niladri +2
Computer Science · Engineering · Mathematics · #Advanced Wireless Network Optimization #Coding theory and cryptography #Cooperative Communication and Network Coding #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1607.01736
6 pages, 1 figure
arxiv created 2016/07/06 · arxiv updated 2016/07/07
It is known that there exists a network, called as the M-network, which is not scalar linearly solvable but has a vector linear solution for message dimension two. Recently, a generalization of this result has been presented where it has been shown that for any integer m≥ 2, there exists a network which has a (m,m) vector linear solution, but does not have a (w,w) vector linear solution for w<m. This paper presents a further generalization. Specifically, we show that for any positive integers k,n, and m≥ 2, there exists a network which has a (mk,mn) fractional linear solution, but does not have a (wk,wn) fractional linear solution for w<m.