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

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.

💡 Research Summary

This paper investigates the fundamental limits of a discrete memoryless point‑to‑point channel that is affected by a random state sequence, when the transmitter has causal channel state information (CSIT) and the communicating parties are allowed to share arbitrary non‑signaling (NS) resources. Non‑signaling resources include any pre‑shared correlations that cannot by themselves be used to transmit information, such as quantum entanglement, but they may generate stronger-than‑classical correlations when combined with the channel.

The authors first recall the classical results: with causal CSIT the Shannon capacity is (C_{C,ca}= \max_{P_{U,X|U,S}} I(U;Y)) and with non‑causal CSIT the Gelfand‑Pinsker capacity is (C_{C,nc}= \max_{P_{U|S}}