QAM下误差有界译码器的混淆-擦除界

中文摘要 AI 辅助

6G预计将推动超可靠低延迟通信（URLLC）朝着任务关键型服务的严格残余错误目标迈进，其中未检测到的错误和擦除具有根本不同的成本。块错误率（BLER）将块混淆（未检测到的错误）和块擦除混为一谈，而这两者对系统可靠性的影响根本不同。本文将误差有界译码器的混淆和擦除分析扩展到有限块长度（FBL）体制下的方形正交幅度调制（QAM）星座。为了处理QAM的异构符号能量——这使得逐对欧氏距离成为一个分布而非单一值——我们分别通过将该分布压缩到其均方根（RMS）距离并对其上的成对混淆进行平均，推导出块混淆率的解析下界和上界。这些界被证明在平均符号能量和块长度上均单调递减，且递减速率由星座阶数控制。数值结果证实，随着信噪比（SNR）或冗余度的增加，混淆率降至可靠性目标以下多个数量级，使得可检测的擦除成为主要的残余错误。

英文摘要

6G is expected to push ultra-reliable low-latency communication (URLLC) toward stringent residual-error targets for mission-critical services, where undetected errors and erasures carry fundamentally different costs. Block error rate (BLER) conflates block confusions (undetected errors) and block erasures, which have fundamentally different impacts on system reliability. This paper extends the confusion and erasure analysis of error-bounded decoders to square quadrature amplitude modulation (QAM) constellations in the finite blocklength (FBL) regime. To handle QAM's heterogeneous symbol energies - which make the per-pair Euclidean distance a distribution rather than a single value - we derive analytical lower and upper bounds on the block confusion rate by, respectively, collapsing this distribution to its root-mean-square (RMS) distance and averaging the pairwise confusion over it. These bounds are proven to be monotonically decreasing in both the average symbol energy and the blocklength, with the decrease rate governed by the constellation order. Numerical results confirm that as the signal-to-noise ratio (SNR) or redundancy increases, the confusion rate falls many orders of magnitude below the reliability target, leaving detectable erasures as the dominant residual error.

发表机构

• RPTU University Kaiserslautern-Landau（凯泽斯劳滕-兰道理工大学）
• German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）

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