The intuitive sphere-packing argument is used to obtain analytically-tractable closed-form approximations for achievable information rates of coded modulation transmission systems, for which only analytically-intractable expressions are available in the literature. These approximations provide a number of insights, possess useful properties and facilitate design/optimization of such systems. They apply to constellations of various cardinalities (including large ones), are simple yet reasonably accurate over the whole signal-to-noise ratio range, and compare favorably to the achieved rates of recent state-of-the art experiments.

中文翻译：

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编码调制系统可实现信息速率的简单闭式近似

直观的球体填充参数用于获得编码调制传输系统可实现的信息速率的分析上易处理的封闭形式近似值，文献中仅提供分析上难处理的表达式。这些近似提供了许多见解，拥有有用的特性并促进此类系统的设计/优化。它们适用于各种基数（包括大基数）的星座，在整个信噪比范围内简单但相当准确，并且与最近最先进的实验所达到的速率相比具有优势。