Confusion-Erasure Bounds of Error-Bounded Decoders under QAM
Abstract
6G is expected to push ultra-reliable low-latency communication (URLLC) toward stringent residual-error tar- gets 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. To characterize the confusion rate analyt- ically, we consider an error-bounded decoder with spherical decision regions. We focus on square quadrature amplitude modulation (QAM) constellations in the finite blocklength (FBL) regime. The confusion rate is governed by the Euclidean distances between modulated codewords, whereas the code structure constrains their Hamming distances. To bridge the two metrics, we introduce a typical distance, which represents the Euclidean distance of a codeword pair at a given Hamming distance on average, and relate it to the Hamming distance through a per-symbol squared-distance coefficient. On this basis, we derive a lower bound on the block confusion rate for random codes and an upper bound for codebooks whose minimum Euclidean distance reaches the typical distance at the non-overlapping threshold. We further characterize how both bounds evolve with the average symbol energy and the block- length. Numerical results, validated by an exact computation for short codes, 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.
Related
- Block Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength
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- Joint Source-Channel Coding of Gaussian Sources over Block Erasure Channels: Nonasymptotic Bounds and Channel-Uniform Normal Approximations
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BibTeX
@misc{chen2026confusionerasure,
title = {{Confusion-Erasure Bounds of Error-Bounded Decoders under QAM}},
author = {Wenwen Chen and Bin Han and Hans D. Schotten},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12631},
eprint = {2609.12631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12631},
}
RIS
TY - UNPB
TI - Confusion-Erasure Bounds of Error-Bounded Decoders under QAM
AU - Wenwen Chen
AU - Bin Han
AU - Hans D. Schotten
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12631
UR - https://arxiv.org/abs/2609.12631
AB - 6G is expected to push ultra-reliable low-latency communication (URLLC) toward stringent residual-error tar- gets 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. To characterize the confusion rate analyt- ically, we consider an error-bounded decoder with spherical decision regions. We focus on square quadrature amplitude modulation (QAM) constellations in the finite blocklength (FBL) regime. The confusion rate is governed by the Euclidean distances between modulated codewords, whereas the code structure constrains their Hamming distances. To bridge the two metrics, we introduce a typical distance, which represents the Euclidean distance of a codeword pair at a given Hamming distance on average, and relate it to the Hamming distance through a per-symbol squared-distance coefficient. On this basis, we derive a lower bound on the block confusion rate for random codes and an upper bound for codebooks whose minimum Euclidean distance reaches the typical distance at the non-overlapping threshold. We further characterize how both bounds evolve with the average symbol energy and the block- length. Numerical results, validated by an exact computation for short codes, 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.
ER -