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arXiv 2602.11568cs.ITmath.IT
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非信号辅助的经典信道容量与因果CSIT

Non-signaling Assisted Capacity of a Classical Channel with Causal CSIT

University of California Irvine（加州大学欧文分校）

Yuhang Yao, Syed A. Jafar

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AI总结：

非信号辅助的经典信道在因果CSIT下容量与非因果设置相同，但通过将信道状态提供给接收端可进一步提高最优错误概率。

摘要：

经典信道在发射端具有因果信道状态信息（CSIT）时的非信号（NS）辅助容量被证明为$C^{NS,ca}=\max_{P_{X|S}}I(X;Y\mid S)$，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，这与非因果CSIT设置下的NS辅助容量$C^{NS,nc}=\max_{P_{X|S}}I(X;Y\mid S)$相同，此前已建立。同时，这也与信道状态不仅（因果或非因果）提供给发射端，还提供给接收端的信道容量一致。尽管容量保持不变，但在NS辅助因果CSIT设置下，对于固定信息量和块长，最优错误概率可通过将信道状态提供给接收端进一步提高。这与对应的NS辅助非因果CSIT设置不同，后者指出通过将状态提供给接收端无法进一步提高最优错误概率。

英文摘要：

The non-signaling (NS) assisted capacity of a classical discrete memoryless 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. As a separate result we prove that non-signaling assistance, feedback, and strictly causal CSIT (i.e., transmitter knows only past channel states but not the current or future states), each of which is individually already known to not increase capacity, also cannot increase capacity when they are collectively made available to the transmitter.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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