Thenoisy permutation channelis a useful abstraction introduced by Makur for point-to-point communication networks and biological storage. While the asymptotic capacity results exist for this model, the characterization of the second-order asymptotics is not available. Therefore, we analyze the converse bounds for the noisy permutation channel in thefinite blocklengthregime. To do this, we present a modified minimax meta-converse for noisy permutation channels by symbol relaxation and construct an auxiliary distribution for this bound usingdivergence covering. We then show the strong converse and refined asymptotic expansions. These two conclusions hold for noisy permutation channels with strictly positive matrices (entry-wise). In addition, we obtain computable bounds for the noisy permutation channel with the binary symmetric channel (BSC), including the original computable converse bound based on the modified minimax meta-converse, the asymptotic expansion, and the$\epsilon $-capacityresult. Finally, numerical results show that the normal approximation shows remarkable precision, and our new converse bound is stronger than existing bounds.

Infrared Small Target Detection is a challenging task to separate small targets from infrared clutter background. Recently, deep learning paradigms have achieved promising results. However, these data-driven methods need plenty of manual annotations. Due to the small size of infrared targets, manual annotation consumes more resources and restricts the development of this field. This letter proposed a labor-efficient annotation framework with level set, which obtains a high-quality pseudo mask with only one cursory click. A variational level set formulation with an expectation difference energy functional is designed, in which the zero level contour is intrinsically maintained during the level set evolution. It solves the issue that zero level contour disappearing due to small target size and excessive regularization. Experiments on the NUAA-SIRST and IRSTD-1k datasets demonstrate that our approach achieves superior performance. Code is available athttps://github.com/Li- Haoqing/COM.