Confusions and Erasures of Error-Bounded Block Decoders with Finite Blocklength

2025-12-18

AI Summary

This work systematically distinguishes and quantifies two distinct error types—undetected confusions and detectable erasures—in block decoders operating over AWGN channels under finite blocklength (FBL) constraints. Conventional block error rate (BLER) metrics conflate these errors, while cross-layer protocols often implicitly assume physical-layer failures manifest as erasures, lacking rigorous FBL-theoretic justification. We establish, for the first time in the FBL regime, analytical models for both confusion and erasure probabilities, leveraging maximum-likelihood decoding analysis and sphere-packing arguments to derive tight upper and lower bounds. We further characterize their dependence on blocklength and SNR. Our theoretical results demonstrate that, for practical FBL codes, the confusion probability is significantly smaller than the erasure probability and becomes negligible at large blocklengths and high SNR. This provides a rigorous, quantitative physical-layer foundation for the widely adopted block-erasure channel model in MAC and network-layer designs.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper investigates two distinct types of block errors - undetected errors (confusions) and erasures - in additive white Gaussian noise (AWGN) channels with error-bounded block decoders operating in the finite blocklength (FBL) regime. While block error rate (BLER) is a common metric, it does not distinguish between confusions and erasures, which can have significantly different impacts in cross-layer protocol design, despite upper-layer protocols universally assuming physical (PHY) errors manifest as packet erasures rather than undetected corruptions - an assumption lacking rigorous PHY-layer validation. We present a systematic analysis of confusions and erasures under BLER-constrained maximum likelihood (ML) decoding. Through sphere-packing analysis, we provide analytical bounds for both block confusion and erasure probabilities, and derive the sensitivities of these bounds to blocklength and signal-to-noise ratio (SNR). To the best of our knowledge, this is the first study on this topic in the FBL regime. Our findings provide theoretical validation for the block erasure channel abstraction commonly assumed in medium access control (MAC) and network layer protocols, confirming that, for practical FBL codes, block confusions are negligible compared to block erasures, especially at large blocklengths and high SNR.

Problem

• Analyzes confusion and erasure errors in AWGN channels with finite blocklength decoders.
• Distinguishes between undetected errors and erasures for cross-layer protocol design.
• Validates the block erasure channel abstraction used in MAC and network layers.

Innovation

• Analyzes block confusion and erasure probabilities via sphere-packing
• Derives bounds sensitivity to blocklength and signal-to-noise ratio
• Validates erasure channel abstraction for upper-layer protocols