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

TL;DR

This paper develops a capacity-achieving feedback scheme for dirty paper channels with state estimation at the receiver, extending it to multiple access channels and noisy state observations, enhancing low-complexity coding strategies.

Contribution

It introduces a novel SK-type feedback scheme that achieves capacity for dirty paper channels with state estimation and extends it to multiple access and noisy observation scenarios.

Findings

Proposed a capacity-achieving feedback scheme for DPC-SE-R.

Extended the scheme to dirty paper multiple-access channels.

Discussed potential extension to noisy state observation cases.

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.