Feedback Capacity of Stationary Gaussian Channels: An Optimal Schalkwijk-Kailath Scheme
Abstract
We consider channels with additive colored Gaussian noise and noiseless feedback. Kim's seminal work derived a stationary variational characterization of feedback capacity and further asserted that the capacity-achieving stationary input need not contain a feedback-independent Gaussian component. These results led to the construction of a simple coding scheme, based on the Schalkwijk--Kailath (SK) refinement principle, which was shown to be capacity-achieving. A recent note identified a gap in the proof of the feedback-independent component-removal assertion, thereby leaving the optimality of the SK scheme and subsequent results that rely on it incomplete. In this paper, we prove the component-removal assertion for channels with stationary Gaussian noise that has a rational power spectral density. Our proof uses a perturbation analysis of a convex optimization formulation of feedback capacity and, indeed, shows that every optimizer assigns zero power to the feedback-independent component. Using this stronger property, we construct from any optimizer an explicit SK coding scheme that achieves every rate below feedback capacity with doubly-exponentially decaying maximal error probability.
Related
- Energy-constrained two-way capacity bounds for noisy Gaussian channels
- A Hardy-Space Proof of the Filter-Only Gaussian Feedback-Capacity Formula
- Classical Capacity of Single-Mode Bosonic Gaussian Channels
- Hamiltonian stationary Lagrangian surfaces of constant Gaussian curvature in complex space forms
- Sharp Stationary Gaussian Approximation for Constant-Stepsize SGD
BibTeX
@misc{fay2026feedback,
title = {{Feedback Capacity of Stationary Gaussian Channels: An Optimal Schalkwijk-Kailath Scheme}},
author = {David Fay and Oron Sabag},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12069},
eprint = {2609.12069},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12069},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Feedback Capacity of Stationary Gaussian Channels: An Optimal Schalkwijk-Kailath Scheme
AU - David Fay
AU - Oron Sabag
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12069
UR - https://arxiv.org/abs/2609.12069
AB - We consider channels with additive colored Gaussian noise and noiseless feedback. Kim's seminal work derived a stationary variational characterization of feedback capacity and further asserted that the capacity-achieving stationary input need not contain a feedback-independent Gaussian component. These results led to the construction of a simple coding scheme, based on the Schalkwijk--Kailath (SK) refinement principle, which was shown to be capacity-achieving. A recent note identified a gap in the proof of the feedback-independent component-removal assertion, thereby leaving the optimality of the SK scheme and subsequent results that rely on it incomplete. In this paper, we prove the component-removal assertion for channels with stationary Gaussian noise that has a rational power spectral density. Our proof uses a perturbation analysis of a convex optimization formulation of feedback capacity and, indeed, shows that every optimizer assigns zero power to the feedback-independent component. Using this stronger property, we construct from any optimizer an explicit SK coding scheme that achieves every rate below feedback capacity with doubly-exponentially decaying maximal error probability.
ER -