An open question posed by Fawzi and Ferme [Transactions on Information Theory 2024], asks whether non-signaling (NS) assistance can increase the capacity of a broadcast channel (BC). We answer this question in the affirmative, by showing that for a certain K-receiver BC setting, called Coordinated Multipoint (CoMP) that arises naturally in wireless networks, NS-assistance provides multiplicative gains in capacity and degrees of freedom (DoF), even achieving K-fold improvements in some cases. Somewhat surprisingly, this is shown to be true even for 2-receiver broadcast channels that are semi-deterministic and/or degraded. In a CoMP BC, B single-antenna transmitters, supported by a backhaul that allows them to share data, act as one B-antenna transmitter, to send independent messages to K receivers, each equipped with a single receive antenna. A fixed and globally known connectivity matrix M, specifies for each transmit antenna, the subset of receivers that are connected to (have a non-zero channel coefficient to) that antenna. Besides the connectivity, there is no channel state information at the transmitter. The DoF region is fully characterized for a class of connectivity patterns associated with tree graphs. Sum-capacity with NS-assistance for arbitrary connectivity patterns is bounded below and above by the triangle number and the min-rank of the connectivity matrix, respectively. While translations to Gaussian settings are demonstrated, most of our results are presented under noise-free, finite-field (Fq) models. Converse proofs for classical DoF adapt the Aligned Images bounds to the finite field model. Converse bounds for NS-assisted capacity extend the same-marginals property to the BC with NS-assistance available to all parties. Even stronger (unbounded) gains are established for certain 'communication with side-information' settings, such as the fading dirty paper channel.

翻译：Fawzi与Ferme在《信息论汇刊2024》中提出的开放性问题，探讨非信号（NS）辅助能否提升广播信道（BC）的容量。我们对此问题给出肯定答案，通过研究表明：在无线网络中自然出现的、称为协调多点（CoMP）的K接收机广播信道场景下，NS辅助能在容量与自由度（DoF）上带来乘性增益，某些情况下甚至可实现K倍提升。令人惊讶的是，这一结论对于半确定性及/或退化型双接收机广播信道同样成立。在CoMP广播信道中，B个单天线发射机通过支持数据共享的回程网络协同工作，等效为一个B天线发射机，向K个配备单接收天线的接收机发送独立消息。固定且全局已知的连接矩阵M规定了每个发射天线所连接的接收机子集（即具有非零信道系数的接收机）。除连接关系外，发射端无信道状态信息。我们完整刻画了与树图相关的一类连接模式下的自由度区域。对于任意连接模式，NS辅助下的和容量下界与上界分别由连接矩阵的三角数与最小秩给出。虽然研究展示了向高斯场景的推广，但主要结果基于无噪声有限域（Fq）模型给出。经典自由度的逆证明将"对齐图像界"适配至有限域模型，而NS辅助容量的逆证明则将相同边际性质扩展至所有参与方均具备NS辅助的广播信道。在某些"带边信息的通信"场景（如衰落脏纸信道）中，我们进一步建立了更强（无界）的增益。