Generalized Schalkwijk-Kailath Coding for Autoregressive Gaussian Channels
Information Theory
2026-02-24 v2 math.IT
Abstract
We propose a Gaussian random coding scheme for AR() Gaussian channels that generalizes the celebrated Schalkwijk-Kailath (SK) coding scheme. This constructive coding scheme, termed the SK(2) coding scheme, yields a closed-form characterization for the corresponding achievable rate. Among many others, this result shows that the celebrated SK coding scheme is not universally optimal, and therefore, disprove the conjecture proposed by Butman in \cite{butman1976linear}.
Cite
@article{arxiv.2601.09329,
title = {Generalized Schalkwijk-Kailath Coding for Autoregressive Gaussian Channels},
author = {Jun Su and Guangyue Han and Shlomo Shamai},
journal= {arXiv preprint arXiv:2601.09329},
year = {2026}
}