Row-Boosted Ensemble Belief Propagation for Short LDPC Codes

2026-08-10

AI Summary

Short-length LDPC codes under belief propagation (BP) decoding are prone to finite-length graph effects, often leading to erroneous or oscillatory decoding trajectories that limit performance. This work proposes a row-based enhancement (RBE) decoding method that introduces effective decoding diversity with minimal overhead by selectively amplifying outgoing messages from only a few parity-check rows, without modifying the parity-check matrix, scheduling strategy, or subcode structure. RBE represents the first efficient ensemble decoding approach based on partial row message enhancement, enabling flexible trade-offs between performance and complexity. On the 5G NR BG1 (144,96) code, a 32-member RBE ensemble reduces the BP-20 frame error rate from 1.6×10⁻² to 1.6×10⁻³ at Eb/N₀ = 4.0 dB, outperforming ensemble schemes of comparable size based on saturated min-sum and affine subcodes, while maintaining consistent gains across various code lengths, rates, and scheduling strategies.

Abstract

Belief-propagation (BP) decoding of short and moderate-length low-density parity-check (LDPC) codes is limited by finite-length graph effects: a single decoder trajectory can become trapped or oscillatory even when an alternative trajectory would decode the received word. Existing ensemble-BP decoders create the required diversity through multiple parity-check matrices, automorphisms, modified schedules, subcodes, or altered update rules. We introduce row-boosted ensemble (RBE) decoding as a minimal decoder-side diversity mechanism: all ensemble members share the same parity-check matrix and the same BP kernel, and differ only in a small set of parity-check rows whose outgoing messages are boosted. On the 5G~NR BG1 \((144,96)\) code, RBE with \(32\) members lowers the frame-error rate of BP with \(20\) iterations (BP-20) from \(1.6\times10^{-2}\) to \(1.6\times10^{-3}\) at \(E_\mathrm{b}/N_0=4.0\,\mathrm{dB}\), outperforming saturated-min-sum and affine subcode ensembles of equal size. Increasing the ensemble size yields additional gains, indicating that RBE provides a scalable performance-complexity tradeoff. The gains transfer across 5G~NR block lengths and rates, to non-5G short LDPC codes, and across flooding and layered schedules.

Problem

• LDPC codes
• belief propagation
• finite-length effects
• decoding failure
• short codes

Innovation

• Row-Boosted Ensemble
• Belief Propagation
• LDPC Codes
• Decoder Diversity
• Finite-Length Effects