Non-signaling Assisted Capacity of a Classical Channel with Causal CSIT
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arXiv
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| Format: | Preprint |
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2026
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| author | Yao, Yuhang Jafar, Syed A. |
| author_facet | Yao, Yuhang Jafar, Syed A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11568 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-signaling Assisted Capacity of a Classical Channel with Causal CSIT Yao, Yuhang Jafar, Syed A. Information Theory 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. |
| title | Non-signaling Assisted Capacity of a Classical Channel with Causal CSIT |
| topic | Information Theory |
| url | https://arxiv.org/abs/2602.11568 |