Precoding for a Class of Peak-Constrained Dirty Paper Channels with a Discrete State

TL;DR

This paper investigates peak-constrained dirty paper channels with discrete states, proposing new precoding schemes that achieve rates close to capacity and improve bounds in optical wireless broadcast channels.

Contribution

It introduces two novel precoding schemes for discrete-state DPC, enhancing achievable rates and capacity bounds in optical wireless broadcast channels.

Findings

Proposed schemes achieve rates within a small gap to capacity.

New capacity inner bound outperforms existing truncated Gaussian bounds.

Achieves near-capacity performance in two-user Gaussian broadcast channels.

Abstract

The dirty paper channel (DPC) under a peak amplitude constraint arises in an optical wireless broadcast channel (BC), where the state at one receiver is the transmitted signal intended for the other receiver(s). This paper studies a class of peak-constrained DPC that is applicable to the optical wireless BC, where the channel state (i.e, `dirt') takes values from some evenly-spaced grid. For the discrete-state DPC studied this paper, a capacity upper bound is obtained from its state-free counterpart. To lower bound its capacity, classical dirty paper coding schemes are revisited, including Costa's coding for DPC and Tomlinson-Harashima (TH) precoding, which serves as benchmark schemes. To improve the benchmark performance, two new precoding schemes are proposed for the discrete-state DPC. Although the proposed schemes do not achieve the state-free capacity contrary to what is known about the Costa's DPC, achievable rates within a small gap to the state-free capacity are demonstrated for the discrete-state DPC. Using the proposed precoding scheme in a two-user peak-constrained Gaussian BC, a new capacity inner bound (IB) is obtained, and is shown to outperform the truncated Gaussian (TG) based IB and is comparable to the best-known IB.