Multicasting Homogeneous and Heterogeneous Quantum States in Quantum Networks

In this paper, we target the practical implementation issues of quantum multicast networks. First, we design a recursive lossless compression that allows us to control the trade-off between the circuit complexity and the dimension of the compressed quantum state. We give a formula that describes the trade-off, and further analyze how the formula is affected by the controlling parameter of the recursive procedure. Our recursive lossless compression can be applied in a quantum multicast network where the source outputs homogeneous quantum states (many copies of a quantum state) to a set of destinations through a bottleneck. Such a recursive lossless compression is extremely useful in the current situation where the technology of producing large-scale quantum circuits is limited. Second, we develop two lossless compression schemes that work for heterogeneous quantum states (many copies of a set of quantum states) when the set of quantum states satisfies a certain structure. The heterogeneous compression schemes provide extra compressing power over the homogeneous compression scheme. Finally, we realize our heterogeneous compression schemes in several quantum multicast networks, including the single-source multi-terminal model, the multi-source multi-terminal model, and the ring networks. We then analyze the bandwidth requirements for these network models.Comment: 24 pages, 9 figure

A Computable Measure of Algorithmic Probability by Finite Approximations with an Application to Integer Sequences

Given the widespread use of lossless compression algorithms to approximate algorithmic (Kolmogorov-Chaitin) complexity, and that lossless compression algorithms fall short at characterizing patterns other than statistical ones not different to entropy estimations, here we explore an alternative and complementary approach. We study formal properties of a Levin-inspired measure $m$ calculated from the output distribution of small Turing machines. We introduce and justify finite approximations $m_k$ that have been used in some applications as an alternative to lossless compression algorithms for approximating algorithmic (Kolmogorov-Chaitin) complexity. We provide proofs of the relevant properties of both $m$ and $m_k$ and compare them to Levin's Universal Distribution. We provide error estimations of $m_k$ with respect to $m$. Finally, we present an application to integer sequences from the Online Encyclopedia of Integer Sequences which suggests that our AP-based measures may characterize non-statistical patterns, and we report interesting correlations with textual, function and program description lengths of the said sequences.Comment: As accepted by the journal Complexity (Wiley/Hindawi

Data Streams from the Low Frequency Instrument On-Board the Planck Satellite: Statistical Analysis and Compression Efficiency

The expected data rate produced by the Low Frequency Instrument (LFI) planned to fly on the ESA Planck mission in 2007, is over a factor 8 larger than the bandwidth allowed by the spacecraft transmission system to download the LFI data. We discuss the application of lossless compression to Planck/LFI data streams in order to reduce the overall data flow. We perform both theoretical analysis and experimental tests using realistically simulated data streams in order to fix the statistical properties of the signal and the maximal compression rate allowed by several lossless compression algorithms. We studied the influence of signal composition and of acquisition parameters on the compression rate Cr and develop a semiempirical formalism to account for it. The best performing compressor tested up to now is the arithmetic compression of order 1, designed for optimizing the compression of white noise like signals, which allows an overall compression rate = 2.65 +/- 0.02. We find that such result is not improved by other lossless compressors, being the signal almost white noise dominated. Lossless compression algorithms alone will not solve the bandwidth problem but needs to be combined with other techniques.Comment: May 3, 2000 release, 61 pages, 6 figures coded as eps, 9 tables (4 included as eps), LaTeX 2.09 + assms4.sty, style file included, submitted for the pubblication on PASP May 3, 200

Importance of Watermark Lossless Compression in Digital Medical Image Watermarking

Large size data requires more storage space, communication time, communication bandwidth and degrades host image quality when it is embedded into it as watermark. Lossless compression reduces data size better than lossless one but with permanent loss of important part of data. Data lossless compression reduces data size contrast to lossy one without any data loss. Medical image data is very sensitive and needs lossless compression otherwise it will result in erroneous input for the health recovery process. This paper focuses on Ultrasound medical image region of interest(ROI) lossless compression as watermark using different techniques; PNG, GIF, JPG, JPEG2000 and Lempel Ziv Welsh (LZW). LZW technique was found 86% better than other tabulated techniques. Compression ratio and more bytes reduction were the parameters considered for the selection of better compression technique. In this work LZW has been used successfully for watermark lossless compression to watermark medical images in teleradiology to ensure less payload encapsulation into images to preserve their perceptual and diagnostic qualities unchanged. On the other side in teleradiology the extracted lossless decompressed watermarks ensure the images authentication and their lossless recoveries in case of any tamper occurrences

On Lossless Compression of 1-bit Audio Signals

In this paper we consider the problem of lossless compression of 1-bit audio signals. We study the properties of some existing proposed solutions. We also discuss possible improvements. Other methods have been considered, and the results are reported