This letter explores the concept of non-coherent index modulation (IM) in a general setting from the standpoint of coding theory. In doing so, we establish a bijective mapping from the set of activation patterns of an IM system to the set of codewords of a binary block code. We show that a non-coherent IM system whose active indices are independently affected by additive white Gaussian noise and Rayleigh fading can achieve a diversity order of $t+1$ if its activation patterns follow a $t$ -error correcting code designed for a Z-channel. Activation codes employed for IM systems are either constant or variable-weight codes. Using a variable-weight code requires a slightly higher detection complexity, but it can result in a diversity order significantly higher than the maximum achievable diversity order of a constant-weight code.

中文翻译：

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非相干索引调制的代码设计

这封信从编码理论的角度探讨了一般环境中非相干索引调制 (IM) 的概念。在这样做时，我们建立了从 IM 系统的激活模式集到二进制块代码的码字集的双射映射。我们表明，一个非相干 IM 系统的活动指数独立受加性高斯白噪声和瑞利衰落影响，可以实现分集阶数为 $t+1$ 如果它的激活模式遵循 $t$ - 专为 Z 通道设计的纠错码。用于 IM 系统的激活代码是恒定或可变权重代码。使用可变权重码需要稍高的检测复杂度，但它可能导致分集阶数明显高于恒定权重码的最大可实现分集阶数。