Achievability Bounds of Coding with Finite Blocklength for Gaussian Broadcast Channels

TL;DR

This paper investigates the limits of coding performance for Gaussian broadcast channels with finite blocklengths, proposing new bounds based on dependence testing and $$ bounds to evaluate achievable rates.

Contribution

It introduces two novel achievability bounds for dirty paper coding in Gaussian broadcast channels with finite blocklength, extending existing theoretical frameworks.

Findings

Dependence testing bound adapted for broadcast channels

Introduction of $$ lower bounds on code sizes

Enhanced understanding of finite blocklength performance limits

Abstract

In this paper, we study the achievable performance of dirty paper coding for the Gaussian broadcast channel (BC) with finite blocklength and we propose two different achievability bounds for this problem. We present the broadcast adaptation of dependence testing bound of Polyanskiy et al. 2010, which is an upper bound on the average error probability that depends on the channel dispersion terms of each error event for fixed input. Additionally, we introduce the $\kappa \beta$ lower bounds on the maximal code sizes of each user using dirty paper coding.