On the universality of the LZ-based decoding algorithm

Cover title.Includes bibliographical references (p. 27).Supported by NSF Faculty Early Career Development (CAREER) Program.Lapidoth, A., Ziv, J

A Universal Decoder Relative to a Given Family of Metrics

Consider the following framework of universal decoding suggested in [MerhavUniversal]. Given a family of decoding metrics and random coding distribution (prior), a single, universal, decoder is optimal if for any possible channel the average error probability when using this decoder is better than the error probability attained by the best decoder in the family up to a subexponential multiplicative factor. We describe a general universal decoder in this framework. The penalty for using this universal decoder is computed. The universal metric is constructed as follows. For each metric, a canonical metric is defined and conditions for the given prior to be normal are given. A sub-exponential set of canonical metrics of normal prior can be merged to a single universal optimal metric. We provide an example where this decoder is optimal while the decoder of [MerhavUniversal] is not.Comment: Accepted to ISIT 201

The implementation of a lossless data compression module in an advanced orbiting system: Analysis and development

Data compression has been proposed for several flight missions as a means of either reducing on board mass data storage, increasing science data return through a bandwidth constrained channel, reducing TDRSS access time, or easing ground archival mass storage requirement. Several issues arise with the implementation of this technology. These include the requirement of a clean channel, onboard smoothing buffer, onboard processing hardware and on the algorithm itself, the adaptability to scene changes and maybe even versatility to the various mission types. This paper gives an overview of an ongoing effort being performed at Goddard Space Flight Center for implementing a lossless data compression scheme for space flight. We will provide analysis results on several data systems issues, the performance of the selected lossless compression scheme, the status of the hardware processor and current development plan

Quantum information and statistical mechanics: an introduction to frontier

This is a short review on an interdisciplinary field of quantum information science and statistical mechanics. We first give a pedagogical introduction to the stabilizer formalism, which is an efficient way to describe an important class of quantum states, the so-called stabilizer states, and quantum operations on them. Furthermore, graph states, which are a class of stabilizer states associated with graphs, and their applications for measurement-based quantum computation are also mentioned. Based on the stabilizer formalism, we review two interdisciplinary topics. One is the relation between quantum error correction codes and spin glass models, which allows us to analyze the performances of quantum error correction codes by using the knowledge about phases in statistical models. The other is the relation between the stabilizer formalism and partition functions of classical spin models, which provides new quantum and classical algorithms to evaluate partition functions of classical spin models.Comment: 15pages, 4 figures, to appear in Proceedings of 4th YSM-SPIP (Sendai, 14-16 December 2012