High-rate product codes (PCs) and staircase codes (SCs) are ubiquitous codes in high-speed optical communication achieving near-capacity performance on the binary symmetric channel. Their success is mostly due to very efficient iterative decoding algorithm that require very little complexity. In this paper, we extend the density evolution (DE) analysis for PCs and SCs to a channel with ternary output and ternary message passing, where the third symbol marks an erasure. We investigate the performance of a standard error-and-erasure decoder and of its simplification using DE. The proposed analysis can be used to find component code configurations and quantizer levels for the channel output. We also show how the use of even-weight BCH subcodes as component codes can improve the decoding performance at high rates. The DE results are verified by Monte-Carlo simulations, which show that additional coding gains of up to 0.6 dB are possible by ternary decoding, at only a small additional increase in complexity compared to traditional binary message passing.

翻译：高标准产品编码(PCs)和楼梯编码(SCs)是高速光学通信中无处不在的编码,在二进制对称信道上达到近容量性能。它们的成功主要归功于非常高效的迭代解码算法,需要的复杂程度很少。在本文中,我们将PCs和SCs的密度演化分析扩大到一个具有长期输出和永久信息传递标志的频道,第三个符号标志着消退。我们调查标准误差和衰变解码的性能及其使用DE的简化。提议的分析可用于为频道输出找到组件代码配置和量测值级别。我们还展示了使用双量 BCH 子编码作为元代码如何以高速改进解码性能。 蒙特-卡洛模拟证实了DE的结果,它表明通过解码,与传统的二元信息传递相比,最多为0.6 dB的额外编码收益可以通过离层解码来增加,只有少量的复杂程度。