The Dispersion of Broadcast Channels With Degraded Message Sets Using Gaussian Codebooks

TL;DR

This paper analyzes the finite blocklength performance of a two-user broadcast channel with degraded message sets using spherical codebooks, considering non-Gaussian noise and fading, and compares decoding schemes under different error criteria.

Contribution

It derives second-order achievable rate regions for non-Gaussian noise and fading scenarios using spherical codebooks, revealing that SIC and JNN decoding perform similarly at finite blocklengths.

Findings

Second-order rate regions are identical for SIC and JNN decoding.

Outage capacity region remains accurate at finite blocklengths.

Spherical codebooks effectively handle non-Gaussian noise and fading.

Abstract

We study the two-user broadcast channel with degraded message sets and derive second-order achievability rate regions. Specifically, the channel noises are not necessarily Gaussian and we use spherical codebooks for both users. The weak user with worse channel quality applies nearest neighbor decoding by treating the signal of the other user as interference. For the strong user with better channel quality, we consider two decoding schemes: successive interference cancellation (SIC) decoding and joint nearest neighbor (JNN) decoding. We adopt two performance criteria: separate error probabilities (SEP) and joint error probability (JEP). Counterintuitively, the second-order achievable rate regions under both SIC and JNN decoding are identical although JNN decoding usually yields better performance in other multiterminal problems with Gaussian noise. Furthermore, we generalize our results to the case with quasi-static fading and show that the asymptotic notion of outage capacity region is an accurate performance measure even at finite blocklengths.