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Low-complexity Ordered Statistic Decoding Algorithm Based on Skipping Mechanisms
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DOI：10.11999/JEIT250447.png)
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Abstract
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Objective Ultra-Reliable Low-Latency Communication (URLLC) in 5G and the emerging Hyper-Reliable Low-Latency Communication (HRLLC) in 6G impose exceptionally stringent requirements on both reliability and end-to-end delay. These requirements create opportunities and challenges for short-length channel codes, particularly in scenarios where Maximum-Likelihood (ML) or near-ML decoding is desirable but computational complexity and latency are prohibitive. Ordered Statistic Decoding (OSD) is a universal near-ML decoding technique that can closely approach finite-length performance bounds. However, its re-encoding step suffers from combinatorial explosion, resulting in impractical complexity in high-throughput and low-latency systems. The excessive number of Test-Error-Pattern (TEP) re-encodings fundamentally restricts the deployment of OSD in URLLC and HRLLC contexts. To address this bottleneck, we design multiple efficient skip mechanisms that substantially reduce re-encoding operations while maintaining negligible performance degradation. Methods Three complementary skipping mechanisms are developed to prune the OSD re-encoding search: (1) Soft-information based skipping. Two criteria are introduced-Trivial and Dynamic Approximate Ideal (DAI), to compare the soft metric of each TEP against the minimum soft weight in the current list. Candidates with excessively large soft weights, which are unlikely to be correct, are skipped. Unlike prior work that evaluates only the first TEP at each Hamming weight increment, both criteria are applied to every candidate. The Trivial criterion ensures no performance loss by skipping only when a TEP's soft metric exceeds the best-so-far. The DAI criterion incorporates an expected residual soft-weight compensation term over non-basis bits, enabling more aggressive skipping with minimal performance degradation. (2) Extra-parity skipping. The search dimension is expanded from k to k + delta by appending the delta most reliable non-basis bit positions to the test vector. Additional parity checks arising from the extended generator matrix eliminate invalid TEPs. Any candidate failing these extra parity constraints is bypassed. (3) Joint skipping. This approach integrates the two preceding mechanisms. Each partial TEP is first tested using the DAI rule and then (e(L), e(delta)) is an element of F-2(k+delta) subjected to the extra-parity check. Only candidates passing both criteria are re-encoded. Results and Discussions Extensive simulations on extended BCH [128, 64] and BCH [127, 64] codes over the BPSK-AWGN channel demonstrate the efficacy of the proposed skipping mechanisms. Soft-information skipping: When compared with conventional OSD using maximum flipping order t = 4 , the Trivial rule is found to reduce average re-encodings by 50%similar to 90% across the SNR range. The DAI rule achieves an additional 60%similar to 99% reduction beyond the Trivial rule. At SNR = 3 dB, the average number of re-encodings decreases from approximately 6.7 x 10(5) to 1.2 x 10(3), with negligible degradation in Frame-Error Rate(FER)(Fig.1). Extra-parity skipping: For delta = 4 , over 90% of re-encodings are eliminated uniformly across SNR values, thereby reducing dependence on channel conditions. This reduction is achieved without significant FER loss (Fig. 2). Joint skipping: The combined mechanism demonstrates superior performance over individual schemes. It reduces average re-encodings by an additional about 40% compared with the DAI rule alone, and by more than 99. 9% compared with extra-parity alone in high-SNR regimes. In this region, re-encodings decrease from similar to 6.7 x 10(5) to fewer than 100, while FER remains nearly identical to that of baseline OSD (Fig. 3). The joint skipping mechanism is further evaluated on BCH codes with different rates, including [127, 36] [127, 64], and [127, 92]. In all cases, substantial reductions in re-encodings are consistently achieved with negligible performance degradation (Fig. 4). A comparative analysis with state-of-the-art schemes-including Probabilistic Sufficient/Necessary Conditions (PSC/PNC), Fast OSD (FOSD), and Order-Skipping OSD (OS-OSD)-shows that the proposed joint skipping OSD with delta = 4 achieves the lowest re-encoding count. Up to two orders of magnitude fewer re-encodings are observed relative to OS-OSD at low SNR, and superiority over FOSD is maintained at moderate SNR, while error-correction performance is preserved across all tested SNRs (Fig. 5). Conclusions To address the stringent reliability and latency requirements of 5G URLLC and future 6G HRLLC, this work presents novel skipping mechanisms for OSD that substantially reduce re-encoding complexity. For offline pre-computed TEPs, the soft-information, extra-parity, and joint skipping rules eliminate more than 99% of redundant re-encodings in typical operating regimes with negligible degradation in Frame-Error Rate (FER). In particular, the proposed joint skipping mechanism lowers the average re-encoding count from approximately to only tens in the high-SNR region, there by meeting practical latency 6.7 x 10(5) constraints while preserving near-ML performance. These findings demonstrate the potential of the proposed skipping framework to enable high-performance short-block decoding in next-generation HRLLC.
Keywords:
Channel decoding
Ordered Statistic Decoding (OSD)
Skipping mechanism
Extra-parity check
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