Exploiting Matrix Information Geometry for Integrated Decoding of Massive Uncoupled Unsourced Random Access

TL;DR

This work tackles latency in uncoupled unsourced random access (UURA) for 6G by introducing MIG-aided integrated decoding, which performs sub-slot codeword detection and stitching simultaneously. By modeling codeword covariances on the HPD manifold and using geodesic distances, the method groups covariance samples from the same active UE across sub-slots to stitch messages in real time. The approach casts decoding as a sparse, ML-informed objective augmented with sparsity and stitching regularizers and solves it via proximal gradient with Douglas-Rachford splitting, achieving favorable complexity and an $\mathcal{O}(1/t)$ convergence rate. Numerical results demonstrate that MIG-aided integrated decoding outperforms CURA and UURA-SD across SNRs, codeword lengths, and antenna regimes, while reducing computation and enabling timely decoding in massive IoT scenarios. This setup offers a practical pathway to low-latency, scalable random access in 6G networks without relying on parity-based stitching bits.

Abstract

In this paper, we explore an efficient uncoupled unsourced random access (UURA) scheme for 6G massive communication. UURA is a typical framework of unsourced random access that addresses the problems of codeword detection and message stitching, without the use of check bits. Firstly, we establish a framework for UURA, allowing for immediate decoding of sub-messages upon arrival. Thus, the processing delay is effectively reduced due to the decreasing waiting time. Next, we propose an integrated decoding algorithm for sub-messages by leveraging matrix information geometry (MIG) theory. Specifically, MIG is applied to measure the feature similarities of codewords belonging to the same user equipment, and thus sub-message can be stitched once it is received. This enables the timely recovery of a portion of the original message by simultaneously detecting and stitching codewords within the current sub-slot. Furthermore, we analyze the performance of the proposed integrated decoding-based UURA scheme in terms of computational complexity and convergence rate. Finally, we present extensive simulation results to validate the effectiveness of the proposed scheme in 6G wireless networks.

Figures (9)

• Figure 1: The proposed UURA framework.
• Figure 2: The illustration of the proposed integrated decoding algorithm. The codeword detection and stitching are performed simultaneously during the solving of P1 by the receiver. Specifically, in the $l$-th sub-slot (e.g., $l=4$ or $5$ shown in the figure), the temporary estimated list $\hat{\mathcal{L}}_l^t$ of active codewords is obtained at the beginning of each iteration. For each active codeword $j\in\hat{\mathcal{L}}_l^t$, the class $\mathcal{C}_{\hat{k}}$ with the shortest geodesic distance is determined. Then, the iteration value of the variable $\boldsymbol{\gamma}_l^{t}$ is updated by minimizing the geodesic distance between the covariance matrix $\textbf{R}_j^{l,t}$ of codeword $j$ and the geometric center $\textbf{G}_{\hat{k}}^{l-1}$ of the class $\mathcal{C}_{\hat{k}}$. After convergence, the active codewords in the $l$-th sub-slot are detected and grouped into $\hat{K}_a$ classes. By unmapping the codeword indices in each class to binary bits, the sub-messages can be timely stitched in chronological order.
• Figure 3: The convergence behaviour of the proposed integrated decoding algorithm for different numbers of BS antennas.
• Figure 4: The convergence rate of the proposed integrated decoding algorithm for different step size settings.
• Figure 5: The DER versus SNR for different lengths of codeword and error probabilities of decoding versus SNR for perfect and imperfect $\hat{K}_a$.

Theorems & Definitions (3)

• Lemma 1
• Lemma 2
• Theorem 1