In this study, we propose partitioned complementary sequences (CSs) where the gaps between the clusters encode information bits to achieve low peak-to-average-power ratio (PAPR) orthogonal frequency division multiplexing (OFDM) symbols. We show that the partitioning rule without losing the feature of being a CS coincides with the non-squashing partitions of a positive integer and leads to a symmetric separation of clusters. We analytically derive the number of partitioned CSs for given bandwidth and a minimum distance constraint and obtain the corresponding recursive methods for enumerating the values of separations. We show that partitioning can increase the spectral efficiency (SE) without changing the alphabet of the nonzero elements of the CS, i.e., standard CSs relying on Reed-Muller (RM) code. We also develop an encoder for partitioned CSs and a maximum-likelihood-based recursive decoder for additive white Gaussian noise (AWGN) and fading channels. Our results indicate that the partitioned CSs under a minimum distance constraint can perform similar to the standard CSs in terms of average block error rate (BLER) and provide a higher SE at the expense of a limited signal-to-noise ratio (SNR) loss.

中文翻译：

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用于低 PAPR OFDM 的分区互补序列编码和解码

在这项研究中，我们提出了分区互补序列 (CS)，其中集群之间的间隙对信息位进行编码，以实现低峰均功率比 (PAPR) 正交频分复用 (OFDM) 符号。我们表明，在不失去作为 CS 特征的情况下的分区规则与正整数的非挤压分区重合，并导致集群的对称分离。我们通过分析推导出给定带宽和最小距离约束的分区 CS 的数量，并获得相应的递归方法来枚举间隔值。我们表明，划分可以提高频谱效率 (SE)，而不会改变 CS 的非零元素的字母表，即依赖 Reed-Muller (RM) 代码的标准 CS。我们还开发了用于分区 CS 的编码器和用于加性高斯白噪声 (AWGN) 和衰落信道的基于最大似然的递归解码器。我们的结果表明，最小距离约束下的分区 CS 在平均误块率 (BLER) 方面可以与标准 CS 相似，并以有限的信噪比 (SNR) 损失为代价提供更高的 SE .