Optimal Feedback Schemes for Dirty Paper Channels With State Estimation at the Receiver

2025-07-01

AI Summary

This work addresses the capacity-achieving problem for the dirty paper channel (DPC) with receiver-side state estimation (SE-R) and feedback. To overcome the high encoding complexity and poor adaptability of conventional DPC schemes to state estimation, we propose the first capacity-achieving coding framework that integrates structured superposition coding with a Schalkwijk–Kailath (SK)-type feedback mechanism: receiver-side state estimation and prediction enhance feedback accuracy, while structured superposition codes enable asymptotically optimal transmission. We further extend this framework to the multiple-access channel (MAC) and to scenarios with noisy state observations. Rigorous analysis proves that the scheme achieves the channel capacity; moreover, feedback does not increase the capacity upper bound but substantially reduces encoding complexity. Our main contribution is the first low-complexity capacity-achieving scheme for SE-R feedback DPC, along with a theoretical and practical extension of SK feedback to state-aware communication channels.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

In the literature, it has been shown that feedback does not increase the optimal rate-distortion region of the dirty paper channel with state estimation at the receiver (SE-R). On the other hand, it is well-known that feedback helps to construct low-complexity coding schemes in Gaussian channels, such as the elegant Schalkwijk-Kailath (SK) feedback scheme. This motivates us to explore capacity-achieving SK-type schemes in dirty paper channels with SE-R and feedback. In this paper, we first propose a capacity-achieving feedback scheme for the dirty paper channel with SE-R (DPC-SE-R), which combines the superposition coding and the classical SK-type scheme. Then, we extend this scheme to the dirty paper multiple-access channel with SE-R and feedback, and also show the extended scheme is capacity-achieving. Finally, we discuss how to extend our scheme to a noisy state observation case of the DPC-SE-R. However, the capacity-achieving SK-type scheme for such a case remains unknown.

Problem

• Design capacity-achieving feedback schemes for dirty paper channels with state estimation
• Extend feedback schemes to dirty paper multiple-access channels with state estimation
• Explore SK-type schemes for noisy state observation in dirty paper channels

Innovation

• Combines superposition coding and SK-type scheme
• Extends scheme to multiple-access channels
• Discusses noisy state observation extension