Alternating direction method of multipliers (ADMM) is an efficient implementation of linear programming (LP) decoding for low-density parity-check (LDPC) codes. By adding penalty terms to the objective function of the LP decoding model, ADMM variable node (VN) penalized decoding can suppress the non-integral solutions and improve the frame error rate (FER) performance in the low signal-to-noise ratio (SNR) region. In this paper, we propose a novel ADMM check node (CN) penalized decoding algorithm. Codeword solutions which satisfy all parity-check equations will have smaller penalty values than non-codeword solutions, including the non-integral solutions. We discuss the required properties of CN-penalty functions, propose a few functions that satisfy those properties, and study their performance/complexity trade-offs. We also investigate the convergence properties of the proposed algorithm and prove that its performance is independent of the transmitted codeword. Using Monte Carlo simulations and instanton analysis, we then demonstrate that the proposed CN-penalized decoder outperforms ADMM VN penalized decoders in both waterfall and error floor regions. This comes at the expense of some increase in the decoding complexity.

中文翻译：

---

ADMM 检查节点惩罚解码器的 LDPC 码

乘法器交替方向法 (ADMM) 是低密度奇偶校验 (LDPC) 码线性规划 (LP) 解码的有效实现。通过在LP解码模型的目标函数中加入惩罚项，ADMM变量节点（VN）惩罚解码可以抑制非整数解，提高低信噪比（SNR）下的帧错误率（FER）性能） 地区。在本文中，我们提出了一种新颖的 ADMM 校验节点（CN）惩罚解码算法。满足所有奇偶校验方程的码字解将比非码字解（包括非整数解）具有更小的惩罚值。我们讨论了 CN 惩罚函数所需的属性，提出了一些满足这些属性的函数，并研究了它们的性能/复杂性权衡。我们还研究了所提出算法的收敛特性，并证明其性能与传输的码字无关。然后使用蒙特卡罗模拟和瞬时子分析，我们证明了所提出的 CN-penalized 解码器在瀑布和错误基底区域都优于 ADMM VN 惩罚解码器。这是以增加解码复杂度为代价的。