Sparse Principal Component Analysis (Sparse PCA) is a pivotal tool in data analysis and dimensionality reduction. However, Sparse PCA is a challenging problem in both theory and practice: it is known to be NP-hard and current exact methods generally require exponential runtime. In this paper, we propose a novel framework to efficiently approximate Sparse PCA by (i) approximating the general input covariance matrix with a re-sorted block-diagonal matrix, (ii) solving the Sparse PCA sub-problem in each block, and (iii) reconstructing the solution to the original problem. Our framework is simple and powerful: it can leverage any off-the-shelf Sparse PCA algorithm and achieve significant computational speedups, with a minor additive error that is linear in the approximation error of the block-diagonal matrix. Suppose $g(k, d)$ is the runtime of an algorithm (approximately) solving Sparse PCA in dimension $d$ and with sparsity constant $k$. Our framework, when integrated with this algorithm, reduces the runtime to $\mathcal{O}\left(\frac{d}{d^\star} \cdot g(k, d^\star) + d^2\right)$, where $d^\star \leq d$ is the largest block size of the block-diagonal matrix. For instance, integrating our framework with the Branch-and-Bound algorithm reduces the complexity from $g(k, d) = \mathcal{O}(k^3\cdot d^k)$ to $\mathcal{O}(k^3\cdot d \cdot (d^\star)^{k-1})$, demonstrating exponential speedups if $d^\star$ is small. We perform large-scale evaluations on many real-world datasets: for exact Sparse PCA algorithm, our method achieves an average speedup factor of 100.50, while maintaining an average approximation error of 0.61%; for approximate Sparse PCA algorithm, our method achieves an average speedup factor of 6.00 and an average approximation error of -0.91%, meaning that our method oftentimes finds better solutions.

As one novel approach to realize end-to-end wireless image semantic transmission, deep learning-based joint source-channel coding (deep JSCC) method is emerging in both deep learning and communication communities. However, current deep JSCC image transmission systems are typically optimized for traditional distortion metrics such as peak signal-to-noise ratio (PSNR) or multi-scale structural similarity (MS-SSIM). But for low transmission rates, due to the imperfect wireless channel, these distortion metrics lose significance as they favor pixel-wise preservation. To account for human visual perception in semantic communications, it is of great importance to develop new deep JSCC systems optimized beyond traditional PSNR and MS-SSIM metrics. In this paper, we introduce adversarial losses to optimize deep JSCC, which tends to preserve global semantic information and local texture. Our new deep JSCC architecture combines encoder, wireless channel, decoder/generator, and discriminator, which are jointly learned under both perceptual and adversarial losses. Our method yields human visually much more pleasing results than state-of-the-art engineered image coded transmission systems and traditional deep JSCC systems. A user study confirms that achieving perceptually similar end-to-end image transmission quality, the proposed method can save about 50% wireless channel bandwidth costs.

The recent deep learning-based joint source-channel coding (deep JSCC) framework has shown superior performance on end-to-end wireless image transmission without suffering from the “cliff effect”. However, a fundamental limit of current deep JSCC schemes is that the unbalanced regional importance of the source image has not been explicitly taken into account. It evenly distributes the coding rate to every image patch leading to an evident degradation of the overall coding efficiency. To break this fundamental limit, we propose a novel end-to-end wireless image transmission scheme in this paper. Our scheme integrates the deep JSCC architecture and the quadtree-structured regional rate allocation strategy adopted in the HEVC standard, collected under the name “resolution-adaptive deep JSCC (RaDJSCC)”. Our new architecture perceives the content of the transmitted image and adaptively allocates more channel bandwidth to the complex pixel blocks. Results show that for high-resolution images, the proposed RaDJSCC transmission method generally outperforms the emerging analog transmission schemes using deep JSCC and the digital transmission schemes using classical separated source and channel coding, e.g., BPG + LDPC.

In the conventional bit interleaved polar coded modulation (BIPCM), there exist some mutual information losses due to neglecting the correlations between the bit levels by using the bit interleaver. Based on this, the delayed BIPCM (DBIPCM) architecture is proposed to reduce the information losses in this paper. In the DBIPCM scheme, only one encoder is adopted and the transmitted symbols convey bits from the codewords encoded at different time for each bit level determined by the preset delays, which is different from the BIPCM. As we know, the variance of the bit channel capacities is used to measure the polarization effect under the multilevel polar coded modulation (MLC-PCM) scheme. It is found that the DBIPCM can achieve a more significant polarization effect compared to the MLC-PCM with the same set partitioning (SP) mapping way due to an extra log2m polarization transform process for 2m-ary constellations. From the simulation results by using the 16PAM over the additive white Gaussian noise channels, it is shown that the DBIPCM with Gray mapping can achieve a better performance compared to the conventional BIPCM. In addition to this, the DBIPCM with SP mapping outperforms the MLC-PCM by up to more than 0.6dB.

In this paper, an architecture of constellation shaping for bit-interleaved polar coded modulation (BIPCM) is proposed. Theoretically, the probability distribution of constellation points should be selected according to a continuous Gaussian distribution over Additive White Gaussian Noise (AWGN) channels, which will help to obtain shaping gain. Based on this probabilistic shaping idea, unequiprobable constellations are designed to increase the mutual information. Under the proposed BIPCM architecture, the mapping method has a larger diversity of bit channels that can help to improve the system performance. The mapping way is performed based on the prefix code, which can meet the above property. Simulation results of 16-ary pulse amplitude modulation (16-PAM) over AWGN channels show that the nonequiprobable constellations provide 0.5dB shaping gain compared to the traditional equiprobable constellations.