块擦除信道与块z信道：有界译码器与有限块长

中文摘要 AI 辅助

块错误率是有限块长（FBL）通信中的标准度量，然而它混淆了两种性质不同的失效模式：块混淆（译码器选择错误码字）和块擦除（译码器声明丢失）。高层协议将物理层失效视为擦除，但这种跨层假设缺乏FBL层面的论证。我们针对加性高斯白噪声（AWGN）信道上的有界距离译码器，在有限块长下推导了块混淆概率（BLCP）和块擦除概率（BLEP）的严格上界及配套的下侧估计，将编码问题重新表述为几何球填充问题。我们分析了这些界对块长和信噪比的敏感性，刻画了上界的包络，并推导了闭式Chernoff近似。将模型扩展到空闲传输块，我们给出了虚警概率（FAP）的界，并表明块z信道抽象可从有界译码几何中自然涌现。数值结果证实，混淆概率和虚警概率远低于错误率约束，为协议设计中假设的块擦除信道和块z信道抽象提供了定量的物理层支持。

英文摘要

Block error rate is a standard metric in finite blocklength (FBL) communication, yet it conflates two qualitatively different failure modes: block confusions, where the decoder selects a wrong codeword, and block erasures, where it declares a loss. Higher-layer protocols treat physical-layer failures as erasures, but this cross-layer assumption lacks FBL justification. We derive a rigorous upper bound and a companion lower-side estimate on the block confusion probability (BLCP) and block erasure probability (BLEP) for bounded-distance decoders over additive white Gaussian noise (AWGN) channels at finite blocklength, recasting the coding problem as a geometric sphere packing one. We analyze the sensitivity of these bounds to blocklength and signalto-noise ratio, characterize the envelope of the upper bound, and derive closed-form Chernoff approximations. Extending the model to idle transmission blocks, we bound the false alarm probability (FAP) and show that a block z-channel abstraction emerges from the bounded-decoding geometry. Numerical results confirm that confusion and false alarm probabilities lie far below the error rate constraint, providing quantitative physicallayer support for the block erasure channel and block z-channel abstractions assumed in protocol design.

发表机构

• RPTU University Kaiserslautern-Landau（莱茵兰-普法塔尔凯泽斯劳滕-兰道应用技术大学）
• Wuhan University（武汉大学）
• RWTH Aachen University（亚琛工业大学）
• TU Dresden（德累斯顿工业大学）
• TU Berlin（柏林工业大学）
• Princeton University（普林斯顿大学）
• German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

Submitted to IEEE TCOM