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

TL;DR

This paper analyzes the different impacts of undetected errors and erasures in finite blocklength AWGN channels, providing bounds and validation for the common assumption that errors manifest as erasures rather than confusions.

Contribution

It offers the first systematic analysis of confusions and erasures in the FBL regime, with analytical bounds and sensitivity analysis, validating the block erasure model in practical scenarios.

Findings

Block confusions are negligible compared to erasures at large blocklengths and high SNR.

Analytical bounds for confusion and erasure probabilities are derived.

The study confirms the validity of the block erasure channel abstraction in FBL codes.

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.