A Universal Scheme for Wyner–Ziv Coding of Discrete Sources

We consider the Wyner–Ziv (WZ) problem of lossy compression where the decompressor observes a noisy version of the source, whose statistics are unknown. A new family of WZ coding algorithms is proposed and their universal optimality is proven. Compression consists of sliding-window processing followed by Lempel–Ziv (LZ) compression, while the decompressor is based on a modification of the discrete universal denoiser (DUDE) algorithm to take advantage of side information. The new algorithms not only universally attain the fundamental limits, but also suggest a paradigm for practical WZ coding. The effectiveness of our approach is illustrated with experiments on binary images, and English text using a low complexity algorithm motivated by our class of universally optimal WZ codes

Efficient Universal Noiseless Source Codes

Although the existence of universal noiseless variable-rate codes for the class of discrete stationary ergodic sources has previously been established, very few practical universal encoding methods are available. Efficient implementable universal source coding techniques are discussed in this paper. Results are presented on source codes for which a small value of the maximum redundancy is achieved with a relatively short block length. A constructive proof of the existence of universal noiseless codes for discrete stationary sources is first presented. The proof is shown to provide a method for obtaining efficient universal noiseless variable-rate codes for various classes of sources. For memoryless sources, upper and lower bounds are obtained for the minimax redundancy as a function of the block length of the code. Several techniques for constructing universal noiseless source codes for memoryless sources are presented and their redundancies are compared with the bounds. Consideration is given to possible applications to data compression for certain nonstationary sources

Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning

Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of fault-tolerant logical gates into consideration. Our algorithm re-synthesizes quantum circuits composed of Clifford group and T gates, the latter being typically the most costly gate in fault-tolerant models, e.g., those based on the Steane or surface codes, with the purpose of minimizing both T-count and T-depth. A major feature of the algorithm is the ability to re-synthesize circuits with additional ancillae to reduce T-depth at effectively no cost. The tested benchmarks show up to 65.7% reduction in T-count and up to 87.6% reduction in T-depth without ancillae, or 99.7% reduction in T-depth using ancillae.Comment: Version 2 contains substantial improvements and extensions to the previous version. We describe a new, more robust algorithm and achieve significantly improved experimental result

On the optimality of code options for a universal noiseless coder

A universal noiseless coding structure was developed that provides efficient performance over an extremely broad range of source entropy. This is accomplished by adaptively selecting the best of several easily implemented variable length coding algorithms. Custom VLSI coder and decoder modules capable of processing over 20 million samples per second are currently under development. The first of the code options used in this module development is shown to be equivalent to a class of Huffman code under the Humblet condition, other options are shown to be equivalent to the Huffman codes of a modified Laplacian symbol set, at specified symbol entropy values. Simulation results are obtained on actual aerial imagery, and they confirm the optimality of the scheme. On sources having Gaussian or Poisson distributions, coder performance is also projected through analysis and simulation

Eating your own dog food

As part of its project to develop a new research data management system the University of Lincoln is embracing development practices built around APIs - interfaces to the underlying data and functions of the system which are explicitly designed to make life easy for developers by being machine readable and programmatically accessible