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

2026-02-12

AI Summary

This study investigates the impact of non-signaling (NS) assistance on the capacity and error probability of classical channels under causal channel state information at the transmitter (CSIT). Leveraging information-theoretic techniques and an NS-assisted communication model, the authors demonstrate that with NS assistance, the channel capacity under causal CSIT equals that under non-causal CSIT, specifically $C^{\text{NS,ca}} = \max_{P_{X|S}} I(X;Y|S)$. Moreover, they reveal that when the receiver has knowledge of the channel state, the error probability under causal CSIT can be significantly reduced—a benefit absent in the non-causal setting. These findings underscore the critical role of receiver-side state information in finite-blocklength communication, highlighting a nuanced advantage of causal over non-causal CSIT in practical scenarios with limited code lengths.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search
• Social Networks and Social Media: Computational social science

Abstract

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.

Problem

• non-signaling
• causal CSIT
• channel capacity
• error probability
• classical channel

Innovation

• non-signaling assistance
• causal CSIT
• channel capacity
• error probability
• channel state information