Error bounds clarify risks of undetected errors and erasures in 6g qam communications
Confusion-Erasure Bounds of Error-Bounded Decoders under QAM
Information Theory
Summary
Reliable and fast communication is important for future 6G networks, especially for critical uses where even small errors matter. The authors show that not all errors are the same—some can be detected and cause erasures, while others are silent confusions that are harder to spot. They analyze how these errors behave when using a common signal method called QAM and develop mathematical bounds to understand the chances of getting undetected errors. Their work helps predict when detectable errors dominate, which is important for designing safer communication systems.
What this means in practice
- •For network schedulers: Optimize packet handling by distinguishing erasures from undetected errors to improve reliability predictions in 6G communication.
- •For communication system engineers: Design decoders that prioritize detectable error detection in square QAM modulated transmissions with finite blocklength constraints.
Authors
Wenwen Chen, Bin Han, Hans D. Schotten
Abstract
6G is expected to push ultra-reliable low-latency communication (URLLC) toward stringent residual-error targets 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. This paper extends the confusion and erasure analysis of error-bounded decoders to square quadrature amplitude modulation (QAM) constellations in the finite blocklength (FBL) regime. To handle QAM's heterogeneous symbol energies - which make the per-pair Euclidean distance a distribution rather than a single value - we derive analytical lower and upper bounds on the block confusion rate by, respectively, collapsing this distribution to its root-mean-square (RMS) distance and averaging the pairwise confusion over it. These bounds are proven to be monotonically decreasing in both the average symbol energy and the blocklength, with the decrease rate governed by the constellation order. Numerical results 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.