spatial resolution is computationally expensive and memory intensive, and suffers from limited receptive fields, downsampling operators are common choices, such as strided convolution and max/average pooling. To recover the resolution, upsampling is thus an essential stage for almost all dense prediction tasks. This poses a fundamental question: *What is the principal approach to recover the resolution of a downsampled feature map (decoding)*. A few upsampling operators are proposed. The *deconvolution* operator, a.k.a. transposed convolution, was initially used in [@zeiler2014visualizing] to visualize convolutional activations and introduced to semantic segmentation [@long2015fully], but this operator sometimes can be harmful due to its behavior in producing checkerboard artifacts [@odena2016deconvolution]. To avoid this, a suggestion is the “resize+convolution” paradigm, which has currently become the standard configuration in state-of-the-art semantic segmentation models [@chen18v3; @lin2017refine]. Apart from these, *perforate* [@osendorfer2014image] and *unpooling* [@badrinarayanan2017segnet] generate sparse indices to guide upsampling. The indices are able to capture and keep boundary information, but one issue is that the two operators can induce much sparsity after upsampling. Convolutional layers with large filter sizes must follow for densification. In addition, *periodic shuffling* ($\mathcal{PS}$) was introduced in [@shi2016real] as a fast and memory-efficient upsampling operator for image super-resolution. $\mathcal{PS}$ recovers resolution by rearranging 