Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Wrap-Decoding in Asynchronous Unsourced Multiple Access With and Without Delay Information

Jyun-Sian Wu, Pin-Hsun Lin, Marcel A. Mross, Eduard A. Jorswieck

TL;DR

The paper tackles asynchronous unsourced multiple access with a maximal per-user delay constraint $D_m$ and unknown per-user delays. It introduces wrap-decoding to fuse delayed codewords, enabling a delay-invariant per-user error bound $ ext{PUPE}$ under AWGN with i.i.d. Gaussian codewords, and analyzes both delay-aware and delay-oblivious decoding. Two PUPE upper bounds are derived using RCU, Chernoff, and saddlepoint techniques, one for decoding without delay information and one for decoding with perfect delay information, with the bounds remaining uniform over delay configurations. Numerical results show the wrap-decoder improves energy efficiency relative to worst-case delay scenarios and yields Eb/N0 performance close to the delay-aware baseline, highlighting practical benefits for massive uncoordinated access in realistic networks.

Abstract

An asynchronous $\ka$-active-user unsourced multiple access channel (AUMAC) is a key model for uncoordinated massive access in future networks. We focus on a scenario where each transmission is subject to the maximal delay constraint ($\dm$), and the precise delay of each user is unknown at the receiver. The combined effects of asynchronicity and uncertain delays require analysis over all possible delay-codeword combinations, making the complexity of the analysis grow with $\dm$ and $\ka$ exponentially. To overcome the complexity, we employ a wrap-decoder for the AUMAC and derive a uniform upper bound on the per-user probability of error (PUPE). The numerical result shows the trade-off between energy per bit and the number of active users under various delay constraints. Furthermore, in our considered AUMAC, decoding without explicit delay information is shown to achieve nearly the same energy efficiency as decoding with perfect delay knowledge.

Wrap-Decoding in Asynchronous Unsourced Multiple Access With and Without Delay Information

TL;DR

The paper tackles asynchronous unsourced multiple access with a maximal per-user delay constraint and unknown per-user delays. It introduces wrap-decoding to fuse delayed codewords, enabling a delay-invariant per-user error bound under AWGN with i.i.d. Gaussian codewords, and analyzes both delay-aware and delay-oblivious decoding. Two PUPE upper bounds are derived using RCU, Chernoff, and saddlepoint techniques, one for decoding without delay information and one for decoding with perfect delay information, with the bounds remaining uniform over delay configurations. Numerical results show the wrap-decoder improves energy efficiency relative to worst-case delay scenarios and yields Eb/N0 performance close to the delay-aware baseline, highlighting practical benefits for massive uncoordinated access in realistic networks.

Abstract

An asynchronous -active-user unsourced multiple access channel (AUMAC) is a key model for uncoordinated massive access in future networks. We focus on a scenario where each transmission is subject to the maximal delay constraint (), and the precise delay of each user is unknown at the receiver. The combined effects of asynchronicity and uncertain delays require analysis over all possible delay-codeword combinations, making the complexity of the analysis grow with and exponentially. To overcome the complexity, we employ a wrap-decoder for the AUMAC and derive a uniform upper bound on the per-user probability of error (PUPE). The numerical result shows the trade-off between energy per bit and the number of active users under various delay constraints. Furthermore, in our considered AUMAC, decoding without explicit delay information is shown to achieve nearly the same energy efficiency as decoding with perfect delay knowledge.
Paper Structure (10 sections, 3 theorems, 42 equations, 2 figures)

This paper contains 10 sections, 3 theorems, 42 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System model and preliminaries
  3. Main Results
  4. Decoding Without Delay Information
  5. Decoding With Perfect Delay Information
  6. Numerical Results
  7. Conclusions
  8. Proof of Theorem \ref{['thm CD2']}
  9. Proof of Theorem \ref{['thm CD with delay information']}
  10. Proof of Lemma 1

Key Result

Theorem 1

Fix $0< \mathsf{P} \leq \mathsf{P}'$. There exists an $(n,{\normalfont \textsf{M}}, \epsilon, \normalfont \textsf{K}_{\text{a}},\alpha)-$code for an AUMAC such that the PUPE is upper-bounded as follows. where $T_s\in\left(0,\min\left\{\frac{1}{4t},1\right\}\right)$ such that $g^{(1)}_{{t_s}}(s,t,T_s)=0,$$\underline T_s\in\left(0,\min\left\{\frac{1}{4t},1\right\}\right)$ such that $\bar{T}_s\in\l

Figures (2)

  • Figure 1: A $\normalfont \textsf{K}_{\text{a}}$-active-user AUMAC with $d_{[\normalfont \textsf{K}_{\text{a}}]}\!\!=\![0,\!1,\!2,\!3,\!...,\!\textsf{D}_{\text{m}}]$.
  • Figure 2: The trade-off between $\frac{\text{E}_{\text{b}}}{\text{N}_{\text{0}}}$ and $\normalfont \textsf{K}_{\text{a}}$

Theorems & Definitions (6)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • Theorem 2
  • Lemma 1