Undetected Error Probability in the Short Blocklength Regime: Approaching Finite-Blocklength Bounds with Polar Codes

2025-03-04

IEEE Transactions on Communications

AI Summary

This work investigates the trade-off between undetected error probability (UEP) and total block error probability for short-length polar codes. For the binary-input additive white Gaussian noise (BI-AWGN) channel, we first derive a dual finite-blocklength achievability bound tailored to UEP. We propose a CRC-assisted functional bit allocation scheme and a novel threshold-based detection method grounded in generalized information density, leading to two CA-polar code designs. Theoretical analysis and simulations demonstrate that: (i) under matched channel conditions, the threshold-based detector outperforms the CRC-aided scheme; (ii) under channel mismatch, the CRC-aided scheme exhibits superior robustness; and (iii) both proposed schemes closely approach the derived achievability bound, significantly improving the accuracy of short-code reliability evaluation. This work provides both theoretical foundations and practical coding design paradigms for ultra-reliable low-latency communication (URLLC).

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We analyze the trade-off between the undetected error probability (i.e., the probability that the channel decoder outputs an erroneous message without detecting the error) and the total error probability in the short blocklength regime. We address the problem by developing two new finite blocklength achievability bounds, which we use to benchmark the performance of two coding schemes based on polar codes with outer cyclic redundancy check (CRC) codes -- also referred to as CRC-aided (CA) polar codes. The first bound is obtained by considering an outer detection code, whereas the second bound relies on a threshold test applied to the generalized information density. Similarly, in the first CA polar code scheme, we reserve a fraction of the outer CRC parity bits for error detection, whereas in the second scheme, we apply a threshold test (specifically, Forney's optimal rule) to the output of the successive cancellation list decoder. Numerical simulations performed on the binary-input AWGN channel reveal that, in the short-blocklength regime, the threshold-based approach is superior to the CRC-based approach, both in terms of bounds and performance of CA polar code schemes. We also consider the case of decoding with noisy channel-state information, which leads to a mismatched decoding setting. Our results illustrate that, differently from the previous case, in this scenario, the CRC-based approach outperforms the threshold-based approach, which is more sensitive to the mismatch.

Problem

• Analyze undetected error probability in short blocklength regime
• Develop finite blocklength bounds for CRC-aided polar codes
• Compare CRC-based and threshold-based decoding performance

Innovation

• Developed two finite blocklength achievability bounds
• Used CRC-aided polar codes for error detection
• Applied threshold test to improve decoding accuracy