An open question recently posed by Fawzi and Ferme [Transactions on Information Theory 2024], asks whether non-signaling (NS) assistance can increase the capacity of a general broadcast channel (BC). We answer this question in the affirmative, by showing that for a certain K-receiver BC model, called Coordinated Multipoint broadcast (CoMP BC) that arises naturally in wireless networks, NS-assistance provides multiplicative gains in both capacity and degrees of freedom (DoF), even achieving K-fold improvements in some cases. 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 shown to be bounded below and above by the triangle number and the min-rank of the connectivity matrix, respectively. While translations to Gaussian settings are demonstrated, for simplicity most of our results are presented under noise-free, finite-field (Fq) models. Converse proofs for classical DoF are found by adapting 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. Beyond the BC setting, even stronger (unbounded) gains in capacity due to NS assistance are established for certain 'communication with side-information' settings, such as the fading dirty paper channel.

翻译：Fawzi和Ferme在《信息论汇刊》（2024年）中提出的一个开放性问题，探讨非信号（NS）辅助是否能提升一般广播信道（BC）的容量。我们对此问题给出了肯定回答，通过研究表明：对于一种在无线网络中自然产生的、称为协调多点广播（CoMP BC）的K接收机BC模型，NS辅助能在容量和自由度（DoF）上带来乘性增益，在某些情况下甚至可实现K倍提升。在CoMP BC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个各配备单接收天线的接收机发送独立消息。一个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（即与该天线存在非零信道系数的接收机）。除连接关系外，发射端不掌握信道状态信息。我们完整刻画了与树图相关的一类连接模式下的DoF区域。对于任意连接模式，NS辅助下的和容量被证明介于连接矩阵的三角数与最小秩之间。虽然研究结果可推广至高斯场景，但为简化分析，大部分结论基于无噪声有限域（Fq）模型给出。经典DoF的逆证明通过将“对齐图像界”适配到有限域模型实现。NS辅助容量的逆证明则将“相同边际分布”性质扩展至所有参与方均可获得NS辅助的BC场景。超越BC设定，在某些“带边信息的通信”场景（如衰落脏纸信道）中，NS辅助甚至能带来更强（无界）的容量增益。