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3D point cloud has been widely applied in virtual reality and augmented reality. A complex 3D scene always needs a large number of the point cloud to represent and demands a lot of space to store. Thus, point cloud compression becomes a crucial issue to research. In this paper, we propose a novel lossy geometric compression method of autoencoder based on DCGAN optimization. This method can reconstruct a high-quality point cloud and solves a large area of missing points in the process of compression and decompression. To improve the point cloud codec performance, we propose a multi-scale 3D deconvolution hopping connection structure to obtain a better-quality reconstructed point cloud under low bit rates. Our approach is the first GAN-based point cloud compression algorithm to our knowledge. Compared with state-of-the-art methods on the MVUB dataset, our approach achieves a better rate-distortion performance and visual quality.

In this paper, we give necessary and sufficient conditions for low-density parity-check (LDPC) codes with column-weight three to correct three errors when decoded using hard-decision message-passing decoding. Additionally, we give necessary and sufficient conditions for column-weight-four codes to correct three errors in four iterations of hard-decision message-passing decoding. We then give a construction technique which results in codes satisfying these conditions. We also provide numerical assessment of code performance via simulation results., Comment: 25 pages. 11 Figures. Part of the work was presented at the Information Theory Workshop (ITW), May 5-9 2008, Porto, Portugal. submitted to IEEE Transactions on Information Theory

Compression of digital holograms is a major challenge that needs to be resolved to enable the efficient storage, transmission and rendering of macroscopic holographic signals. In this work, we propose to deploy the wave atom transform that has been utilized before for interferometric modalities such as acoustic and seismic signals. This non-adaptive multi- resolution transform has good space-frequency localization and its orthonormal basis is suitable for sparsifying holographic signals. By replacing the CDF 9/7 wavelet transform stage in a JPEG 2000 codec with the proposed wave atom transform, we did assess its suitability for coding complex amplitude wavefronts. Experimental results demonstrate improved rate-distortion performance with respect to JPEG 2000 and H.265/HEVC for a set of computer-generated, diffuse, macroscopic holograms.

A word $x$ that is absent from a word $y$ is called minimal if all its proper factors occur in $y$. Given a collection of $k$ words $y_1,y_2,\ldots,y_k$ over an alphabet $\Sigma$, we are asked to compute the set $\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{k}}$ of minimal absent words of length at most $\ell$ of word $y=y_1\#y_2\#\ldots\#y_k$, $\#\notin\Sigma$. In data compression, this corresponds to computing the antidictionary of $k$ documents. In bioinformatics, it corresponds to computing words that are absent from a genome of $k$ chromosomes. This computation generally requires $\Omega(n)$ space for $n=|y|$ using any of the plenty available $\mathcal{O}(n)$-time algorithms. This is because an $\Omega(n)$-sized text index is constructed over $y$ which can be impractical for large $n$. We do the identical computation incrementally using output-sensitive space. This goal is reasonable when $||\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{N}}||=o(n)$, for all $N\in[1,k]$. For instance, in the human genome, $n \approx 3\times 10^9$ but $||\mathrm{M}^{12}_{y_{1}\#\ldots\#y_{k}}|| \approx 10^6$. We consider a constant-sized alphabet for stating our results. We show that all $\mathrm{M}^{\ell}_{y_{1}},\ldots,\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{k}}$ can be computed in $\mathcal{O}(kn+\sum^{k}_{N=1}||\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{N}}||)$ total time using $\mathcal{O}(\mathrm{MaxIn}+\mathrm{MaxOut})$ space, where $\mathrm{MaxIn}$ is the length of the longest word in $\{y_1,\ldots,y_{k}\}$ and $\mathrm{MaxOut}=\max\{||\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{N}}||:N\in[1,k]\}$. Proof-of-concept experimental results are also provided confirming our theoretical findings and justifying our contribution., Comment: Version accepted to DCC 2019

We consider a fixed-rate zero-delay source coding problem where a stationary vector-valued Gauss-Markov source is compressed subject to an average mean-squared error (MSE) distortion constraint. We address the problem by considering the Gaussian nonanticipative rate distortion function (NRDF) which is a lower bound to the zero-delay Gaussian RDF. Then, we use its corresponding optimal “test-channel” to characterize the stationary Gaussian NRDF and evaluate the corresponding information rates. We show that the Gaussian NRDF can be achieved by p-parallel fixed-rate scalar uniform quantizers of finite support with dithering signal up to a multiplicative distortion factor and a constant rate penalty. We demonstrate our framework with a numerical example. QC 20180108. QC 20191025