In this letter, we demonstrate a mapper that enables all waveforms of OFDM with Index Modulation (OFDM-IM) while preserving polynomial time and space computational complexities. Enabling all OFDM-IM waveforms maximizes the spectral efficiency (SE) gain over the classic OFDM but, as far as we know, the computational overhead of the resulting mapper remains conjectured as prohibitive across the OFDM-IM literature. We show that the largest number of binomial coefficient calculations performed by the original OFDM-IM mapper is polynomial on the number of subcarriers, even under the setup that maximizes the SE gain over OFDM. Also, such coefficients match the entries of the so-called Pascal's triangle (PT). Thus, by assisting the OFDM-IM mapper with a PT table, we show that the maximum SE gain over OFDM can be achieved under polynomial (rather than exponential) time and space complexities.

中文翻译：

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多项式空间复杂度下具有索引调制的OFDM的最大频谱效率

在这封信中，我们展示了一种映射器，该映射器支持带索引调制 (OFDM-IM) 的 OFDM 的所有波形，同时保留多项式时间和空间计算复杂性。启用所有 OFDM-IM 波形可以最大限度地提高经典 OFDM 的频谱效率 (SE) 增益，但据我们所知，结果映射器的计算开销在整个 OFDM-IM 文献中仍然被认为是令人望而却步。我们表明，原始 O​​FDM-IM 映射器执行的最大数量的二项式系数计算在子载波数量上是多项式的，即使在使 SE 增益超过 OFDM 的设置下也是如此。此外，此类系数与所谓的帕斯卡三角形 (PT) 的条目相匹配。因此，通过使用 PT 表辅助 OFDM-IM 映射器，