We consider a $\sf K$ user interference network with general connectivity, described by a matrix $\mat{N}$, and general message flows, described by a matrix $\mat{M}$. Previous studies have demonstrated that the standard interference scheme (IA) 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 $\mat{M}$ and $\mat{N}$ 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 significantly higher $\SDoF$ than the standard IA scheme.

翻译：我们考虑一个具有一般连通性的 $\sf K$ 用户干扰网络，该网络由矩阵 $\mat{N}$ 描述通用连通性，并由矩阵 $\mat{M}$ 描述通用消息流。先前研究表明，标准干扰对齐方案对于稀疏连通性网络可能并非最优。本文针对给定的 $\mat{M}$ 和 $\mat{N}$，形式化了一种通用干扰对齐编码方案及一个直观的数字填充谜题，使得该谜题解的得分决定了干扰对齐方案可实现的最优和自由度。针对一类一般的对称信道，提出了该谜题的解，并证明该解相比标准干扰对齐方案能显著提升 $\SDoF$。