DoF Analysis for (M, N)-Channels through a Number-Filling Puzzle

We consider a
$\mathrm{K}$
user interference network with general connectivity, described by a matrix N, and general message flows, described by a matrix M. Previous studies have demonstrated that the standard interference alignment (IA) scheme might not be optimal for networks with sparse connectivity. In this paper, we formalize a general IA coding scheme and an intuitive number-filling puzzle for given M and N in a way that the score of the solution to the puzzle determines the optimum sum degrees that can be achieved by the IA scheme. A solution to the puzzle is proposed for a general class of symmetric channels, and it is shown that this solution leads to enhanced Sum-DoF compared to the standard IA scheme.