With the emerging of huge amount of unlabeled data, unsupervised out-of-distribution (OOD) detection is vital for ensuring the reliability of graph neural networks (GNNs) by identifying OOD samples from in-distribution (ID) ones during testing, where encountering novel or unknown data is inevitable. Existing methods often suffer from compromised performance due to redundant information in graph structures, which impairs their ability to effectively differentiate between ID and OOD data. To address this challenge, we propose SEGO, an unsupervised framework that integrates structural entropy into OOD detection regarding graph classification. Specifically, within the architecture of contrastive learning, SEGO introduces an anchor view in the form of coding tree by minimizing structural entropy. The obtained coding tree effectively removes redundant information from graphs while preserving essential structural information, enabling the capture of distinct graph patterns between ID and OOD samples. Furthermore, we present a multi-grained contrastive learning scheme at local, global, and tree levels using triplet views, where coding trees with essential information serve as the anchor view. Extensive experiments on real-world datasets validate the effectiveness of SEGO, demonstrating superior performance over state-of-the-art baselines in OOD detection. Specifically, our method achieves the best performance on 9 out of 10 dataset pairs, with an average improvement of 3.7% on OOD detection datasets, significantly surpassing the best competitor by 10.8% on the FreeSolv/ToxCast dataset pair.

Cubic metric (CM) is being regarded as a more accurate metric for envelope fluctuations of orthogonal frequency division multiplexing (OFDM) signals than peak-to-average power ratio (PAPR). Iterative clipping and filtering (ICF) is a simple and efficient technique for PAPR reduction. However, our analysis shows that this technique can not actually achieve sufficient CM reduction due to the difference between the two metrics. In this paper, based on the definition of CM, a new clipping method called descendent clipping is proposed, which can achieve more CM reduction by introducing a new parameter called descent factor. Further, we combine descendent clipping with filtering and develop two iterative descendent clipping and filtering (IDCF) algorithms: adaptive IDCF and fixed IDCF. Simulation results show that these two algorithms offer better performance and much faster convergence than the conventional ICF technique when used to reduce CM.

Clipping and filtering can be used to effectively reduce the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals at the cost of introducing distortion. So far, various clipping and filtering techniques have been proposed in the literature, which have different performance in terms of PAPR reduction and signal distortion. However, the minimum signal distortion required to achieve a given PAPR level, i.e., the ultimate performance of clipping and filtering techniques, has not been investigated. In this paper, clipping and filtering is interpreted as a procedure of adding an extra signal to the original signal. Based on this, the ultimate performance problem of clipping and filtering techniques can be formulated as a convex optimization problem, by solving which we obtain the ultimate performance of clipping and filtering techniques. Subsequently, using this ultimate performance we evaluate the performance of several famous clipping and filtering techniques and provide the simulation results.