Generalized Schalkwijk-Kailath Coding for Autoregressive Gaussian Channels

TL;DR

This paper introduces a generalized Gaussian coding scheme for autoregressive Gaussian channels, expanding the classical Schalkwijk-Kailath scheme and providing new insights into its optimality and achievable rates.

Contribution

It presents a new constructive coding scheme, SK(2), with a closed-form achievable rate, challenging the universal optimality of the original SK coding scheme.

Findings

The SK(2) coding scheme generalizes the classical SK scheme.

The achievable rate for AR(p) Gaussian channels is explicitly characterized.

The classical SK scheme is shown not to be universally optimal.

Abstract

We propose a Gaussian random coding scheme for AR($p$) 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}.