Movable antennas and reconfigurable intelligent surfaces enable a new paradigm in which channel statistics can be controlled and altered. Further, the known trajectory and operation protocol of communication satellites results in networks with predictable statistics. The predictability of future changes results in a non-ergodic model for which the fundamentals are largely unknown. We consider the canonical two-user broadcast erasure channel in which channel statistics vary at a priori known points. We consider a multi-modal setting with two non-transient modes (whose lengths scale linearly with the blocklength) and an arbitrary number of transient modes. We provide a new set of outer-bounds on the capacity region of this problem when the encoder has access to causal ACK/NACK feedback. The outer-bounds reveal the significant role of the non-transient mode with higher erasure probability both on the outer and the inner bounds. We show the outer-bounds are achievable in non-trivial regimes, characterizing the capacity region for a wide range of parameters. We also discuss the regimes where the inner and outer bounds diverge and analyze the gap between the two. A key finding of this work is the significant gain of inter-modal coding over the separate treating of individual modes.

翻译：可移动天线与可重构智能表面开启了一种新范式，使得信道统计特性能够被控制和改变。此外，通信卫星的已知轨迹与操作协议形成了具有可预测统计特性的网络。未来变化的可预测性导致了一种非遍历模型，其基本特性在很大程度上尚属未知。我们考虑典型的双用户广播擦除信道，其中信道统计特性在事先已知的时间点发生变化。我们研究一种多模态场景，包含两种非瞬态模态（其长度与块长度呈线性比例）以及任意数量的瞬态模态。当编码器能够获取因果性ACK/NACK反馈时，我们针对该问题提出了新的容量区域外边界。这些外边界揭示了具有较高擦除概率的非瞬态模态在内外边界中的重要作用。我们证明了这些外边界在非平凡区域内是可实现的，从而刻画了广泛参数范围内的容量区域。我们还讨论了内外边界分离的区域，并分析了两者之间的差距。本工作的一个关键发现是：跨模态编码相较于单独处理各模态能带来显著增益。