The non-signaling (NS) assisted capacity of a classical channel with causal channel state information at the transmitter (CSIT) is shown to be $C^{NS,ca}=\max_{P_{X|S}}I(X;Y\mid S)$, where $X, Y, S$ correspond to the input, output and state of the channel. Remarkably, this is the same as the capacity of the channel in the NS-assisted non-causal CSIT setting, $C^{NS,nc}=\max_{P_{X|S}}I(X;Y\mid S)$, which was previously established, and also matches the (either classical or with NS assistance) capacity of the channel where the state is available not only (either causally or non-causally) to the transmitter but also to the receiver. While the capacity remains unchanged, the optimal probability of error for fixed message size and blocklength, in the NS-assisted causal CSIT setting can be further improved if channel state is made available to the receiver. This is in contrast to corresponding NS-assisted non-causal CSIT setting where it was previously noted that the optimal probability of error cannot be further improved by providing the state to the receiver.

翻译：本文证明了在发送端具有因果信道状态信息（CSIT）的情况下，经典信道的非信令（NS）辅助容量为 $C^{NS,ca}=\max_{P_{X|S}}I(X;Y\mid S)$，其中 $X, Y, S$ 分别对应信道的输入、输出和状态。值得注意的是，该容量与先前已建立的、在NS辅助下具有非因果CSIT的信道容量 $C^{NS,nc}=\max_{P_{X|S}}I(X;Y\mid S)$ 相同，同时也与信道状态不仅对发送端（无论是因果还是非因果方式）可用、也对接收端可用时的信道容量（无论是经典容量还是NS辅助容量）相匹配。尽管容量保持不变，但在NS辅助的因果CSIT场景中，对于固定消息大小和块长度，若将信道状态提供给接收端，其最优误码概率可得到进一步改善。这与先前指出的、在对应的NS辅助非因果CSIT场景中，向接收端提供状态信息并不能进一步改善最优误码概率的情况形成了对比。