Non-asymptotic Sphere-Packing Bounds for Finite-Blocklength Scalar Gaussian Multiple-Access and Broadcast Channels
Abstract
This paper investigates non-asymptotic achievable rate regions of Gaussian multiple-access channels (MACs) and broadcast channels (BCs) in the finite-blocklength regime. By employing a proposed volume-uniform random coding (VURC) codebook that distributes codewords uniformly within an n-dimensional power sphere, together with successive interference cancellation (SIC) decoding, we derive a closed-form achievability bound, a scheme-specific lower bound on the average error probability, and a fourth-order asymptotic characterization. The proposed SIC achievability bound admits a simple and analytically interpretable closed-form expression, enabling direct performance evaluation without iterative computation. The structure of the proposed SIC asymptotic bound offers a highly extensible framework, allowing advances in single-user finite-blocklength theory to be systematically incorporated into the multiuser setting. Futhermore, to characterize the performance benefit of joint decoding, we further derive numerical and closed-form achievability bounds for the two-user Gaussian MAC under joint nearest-neighbor (JNN) decoding. Numerical results illustrate the performance differences among the proposed SIC and JNN bounds and existing benchmarks.
Related
- Marker-Delimited Codes for Short-Blocklength, High-Rate Coding over Multi-Read Edit Channels
- Quantum Broadcast Channels with Mutually Confidential Messages
- Orbit Reduction and Learned Run Distributions for Finite-Blocklength Binary Deletion Channels
- Rateless Nested Lattice Codes for Secure Cooperative V2X Broadcast over Fading and Erasure Channels
- Second-Order Asymptotics for the Scalar Gaussian Broadcast Channel
BibTeX
@misc{bao2026nonasymptotic,
title = {{Non-asymptotic Sphere-Packing Bounds for Finite-Blocklength Scalar Gaussian Multiple-Access and Broadcast Channels}},
author = {Kaixuan Bao and Wei Xu and Xiaohu You},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04647},
eprint = {2611.04647},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04647},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-asymptotic Sphere-Packing Bounds for Finite-Blocklength Scalar Gaussian Multiple-Access and Broadcast Channels
AU - Kaixuan Bao
AU - Wei Xu
AU - Xiaohu You
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04647
UR - https://arxiv.org/abs/2611.04647
AB - This paper investigates non-asymptotic achievable rate regions of Gaussian multiple-access channels (MACs) and broadcast channels (BCs) in the finite-blocklength regime. By employing a proposed volume-uniform random coding (VURC) codebook that distributes codewords uniformly within an n-dimensional power sphere, together with successive interference cancellation (SIC) decoding, we derive a closed-form achievability bound, a scheme-specific lower bound on the average error probability, and a fourth-order asymptotic characterization. The proposed SIC achievability bound admits a simple and analytically interpretable closed-form expression, enabling direct performance evaluation without iterative computation. The structure of the proposed SIC asymptotic bound offers a highly extensible framework, allowing advances in single-user finite-blocklength theory to be systematically incorporated into the multiuser setting. Futhermore, to characterize the performance benefit of joint decoding, we further derive numerical and closed-form achievability bounds for the two-user Gaussian MAC under joint nearest-neighbor (JNN) decoding. Numerical results illustrate the performance differences among the proposed SIC and JNN bounds and existing benchmarks.
ER -