发表机构
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究为给定迭代解码器设计LDPC码的难题，提出基于确定性GD的框架，直接在松弛原图表示上操作，损失函数基于DE误码率性能，优化过程自主，收敛快速可靠，实验显示优化原图性能优于5G LDPC码。
AI 中文摘要
我们考虑为给定迭代解码器设计低密度奇偶校验（LDPC）码。尽管有直接模拟、密度进化（DE）和EXIT图分析等工具，但选择奇偶校验矩阵仍是困难的组合优化问题。现有方法常依赖基于种群的搜索等，需仔细调参且计算成本高。基于梯度下降（GD）的方法通过解码器模拟微分来优化松弛奇偶校验矩阵，但依赖噪声蒙特卡罗估计等，对长LDPC码成本高。本文聚焦基于原图的长LDPC码设计，提出基于确定性GD的框架，直接在松弛原图表示上操作。损失函数基于DE误码率性能，可直接针对松弛原图评估。通过将松弛表示与二元原图集合关联，证明所提松弛DE给出集合平均DE性能。优化过程完全自主，使用标准GD方法，因确定性DE评估和信息梯度，收敛快速可靠。针对最小和解码器的数值实验表明，优化后的原图优于相同原图维度的5G LDPC码。
英文摘要
We consider the design of low-density parity-check (LDPC) codes for a given iterative decoder. While LDPC performance can be evaluated using simulation, density evolution (DE), or EXIT-chart analysis, selecting a parity-check matrix (PCM) remains a difficult combinatorial optimization problem. Existing approaches often rely on population-based search, random mutations, or genetic algorithms, which require careful tuning and incur high computational cost. Recent gradient descent (GD)-based methods optimize relaxed PCMs by differentiating through decoder simulations, but rely on noisy Monte Carlo estimates, line searches over soft matrix representations, and remain costly for long codes. Moreover, the loss is typically evaluated only at integer-valued PCMs. We focus on long protograph-based LDPC codes and propose a deterministic GD-based framework operating directly on a relaxed protograph representation. The loss is based on DE bit error rate (BER) and can be evaluated directly for relaxed protographs. To justify this relaxation, we associate the relaxed representation with an ensemble of binary PCMs and show that the proposed relaxed DE yields the ensemble-averaged DE performance. The resulting procedure supports standard GD optimization and achieves fast, reliable convergence through deterministic DE evaluation and informative gradients. Numerical results show that the optimized protographs outperform 5G LDPC codes with matching dimensions.
CommentsA short version of this paper has been accepted for presentation at IEEE GLOBECOM 2026 Workshops: Workshop on Channel Coding beyond 5G. This extended version of the paper has been submitted to the IEEE Transactions on Communications journal
