Block Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength

2026-09-23

AI Summary

本文针对有限码长通信中块错误率的问题，通过几何球体填充方法推导了AWGN信道上块混淆概率和块擦除概率的上下界，并分析了其对码长和信噪比的敏感性。

Abstract

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.

Problem

• Block Erasure
• Finite Blocklength
• Bounded Decoders
• Block Confusion
• Block Erasure Channel

Innovation

• Block Confusion Probability
• Block Erasure Probability
• Bounded-Distance Decoders
• Finite Blocklength
• Geometric Sphere Packing