In this paper, we propose a simple method for generating short-length rate-compatible codes that are robust to noncoherent detection forM-PSK constellations. For any given constellation set, first we use a greedy algorithm to construct a family of rotationally invariant codes. Then, by properly modifying such codes, we obtain a new family of codes that are robust to noncoherent detection. We briefly discuss the optimality of the constructed codes for special cases of BPSK and QPSK constellations. Our method provides an upper bound for the length of optimal codes with a given desired noncoherent distance. We also derive a simple asymptotic upper bound on the frame error rate (FER) of such codes and provide some simulations. Finally, the problem of designing binary codes that are robust to noncoherent detection for QPSK constellation is briefly discussed.

中文翻译：

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用于非相干检测的短码速率兼容代码设计

在本文中，我们提出了一种简单的方法来生成对M 的非相干检测具有鲁棒性的短长度速率兼容代码-PSK 星座。对于任何给定的星座集，首先我们使用贪心算法来构造旋转不变代码族。然后，通过适当修改这些代码，我们获得了一个对非相干检测具有鲁棒性的新代码族。我们简要讨论了 BPSK 和 QPSK 星座特殊情况下构造代码的最优性。我们的方法为具有给定所需非相干距离的最佳代码长度提供了上限。我们还推导出了此类代码的帧错误率 (FER) 的简单渐近上限，并提供了一些模拟。最后，简要讨论了设计对 QPSK 星座的非相干检测具有鲁棒性的二进制代码的问题。