PAM星座笛卡尔幂的球形码软解映射
Soft Demapping of Spherical Codes from Cartesian Powers of PAM Constellations
AI总结：
本文研究光通信中由PAM星座笛卡尔幂构造的球形码软解映射，提出轨道解映射方法，并证明其相比传统逐符号解映射可获得0.1至0.5 dB的信噪比增益。
摘要：
针对光通信系统中级联编码的应用，我们研究了由脉冲幅度调制（PAM）星座的笛卡尔幂的恒定能量壳层构造的短球形码的软解映射。这些码是具有相同平均功率的置换码的并集。我们通过改进Murty算法为置换码构造了一个列表译码器，并利用该译码器确定这些置换码的互信息曲线。在此过程中，我们发现了一个简洁的表达式，用于确定置换码中被称为轨道的大子码的似然。我们引入了一个简单的过程，称为轨道解映射，使我们能够从含噪的置换码字中提取软信息。在一个采用标准低密度奇偶校验码保护的概率幅度整形、并使用短置换码的示例通信系统中，我们证明与传统的逐符号解映射相比，轨道解映射在信噪比方面提供了约0.3 dB的增益。通过使用由置换码并集组成的球形码，与单独使用置换码相比，我们可以提高输入熵。在一种方案中，我们考虑少量置换码的并集。在这种情况下，与传统方法相比，轨道解映射提供了约0.2 dB的增益。在另一种方案中，我们使用所有可能的置换来形成一个球形码，该球形码具有计算上可行的网格表示。使用BCJR算法获得的软信息比传统的逐符号方法性能好0.1 dB。使用包含相同平均功率的所有可能置换码的球形码和BCJR算法，观察到0.5 dB的增益。比特度量译码的可达信息速率比较验证了所观察到的增益。
英文摘要：
For applications in concatenated coding for optical communications systems, we examine soft-demapping of short spherical codes constructed as constant-energy shells of the Cartesian power of pulse amplitude modulation constellations. These are unions of permutation codes having the same average power. We construct a list decoder for permutation codes by adapting Murty's algorithm, which is then used to determine mutual information curves for these permutation codes. In the process, we discover a straightforward expression for determining the likelihood of large subcodes of permutation codes called orbits. We introduce a simple process, called orbit demapping, that allows us to extract soft information from noisy permutation codewords. In a sample communication system with probabilistic amplitude shaping protected by a standard low-density parity-check code that employs short permutation codes, we demonstrate that orbit demapping provides a gain of about 0.3 dB in signal-to-noise ratio compared to the traditional symbol-by-symbol demapping. By using spherical codes composed of unions of permutation codes, we can increase the input entropy compared to using permutation codes alone. In one scheme, we consider a union of a small number of permutation codes. In this case, orbit demapping provides about 0.2 dB gain compared to the traditional method. In another scheme, we use all possible permutations to form a spherical code that exhibits a computationally feasible trellis representation. The soft information obtained using the BCJR algorithm outperforms the traditional symbol-by-symbol method by 0.1 dB. Using the spherical codes containing all possible permutation codes of the same average power and the BCJR algorithm, a gain of 0.5 dB is observed. Comparison of the achievable information rates of bit-metric decoding verifies the observed gains.
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