Parsing a sequence of qubits

We develop a theoretical framework for frame synchronization, also known as block synchronization, in the quantum domain which makes it possible to attach classical and quantum metadata to quantum information over a noisy channel even when the information source and sink are frame-wise asynchronous. This eliminates the need of frame synchronization at the hardware level and allows for parsing qubit sequences during quantum information processing. Our framework exploits binary constant-weight codes that are self-synchronizing. Possible applications may include asynchronous quantum communication such as a self-synchronizing quantum network where one can hop into the channel at any time, catch the next coming quantum information with a label indicating the sender, and reply by routing her quantum information with control qubits for quantum switches all without assuming prior frame synchronization between users.Comment: 11 pages, 2 figures, 1 table. Final accepted version for publication in the IEEE Transactions on Information Theor

Synchronizing Strongly Connected Partial DFAs

We study synchronizing partial DFAs, which extend the classical concept of synchronizing complete DFAs and are a special case of synchronizing unambiguous NFAs. A partial DFA is called synchronizing if it has a word (called a reset word) whose action brings a non-empty subset of states to a unique state and is undefined for all other states. While in the general case the problem of checking whether a partial DFA is synchronizing is PSPACE-complete, we show that in the strongly connected case this problem can be efficiently reduced to the same problem for a complete DFA. Using combinatorial, algebraic, and formal languages methods, we develop techniques that relate main synchronization problems for strongly connected partial DFAs with the same problems for complete DFAs. In particular, this includes the \v{C}ern\'{y} and the rank conjectures, the problem of finding a reset word, and upper bounds on the length of the shortest reset words of literal automata of finite prefix codes. We conclude that solving fundamental synchronization problems is equally hard in both models, as an essential improvement of the results for one model implies an improvement for the other.Comment: Full version of the paper at STACS 202

Some basic properties of fix-free codes.

by Chunxuan Ye.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 74-[78]).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Information Theory --- p.1Chapter 1.2 --- Source Coding --- p.2Chapter 1.3 --- Fixed Length Codes and Variable Length Codes --- p.4Chapter 1.4 --- Prefix Codes --- p.5Chapter 1.4.1 --- Kraft Inequality --- p.7Chapter 1.4.2 --- Huffman Coding --- p.9Chapter 2 --- Existence of Fix-Free Codes --- p.13Chapter 2.1 --- Introduction --- p.13Chapter 2.2 --- Previous Results --- p.14Chapter 2.2.1 --- Complete Fix-Free Codes --- p.14Chapter 2.2.2 --- Ahlswede's Results --- p.16Chapter 2.3 --- Two Properties of Fix-Free Codes --- p.17Chapter 2.4 --- A Sufficient Condition --- p.20Chapter 2.5 --- Other Sufficient Conditions --- p.33Chapter 2.6 --- A Necessary Condition --- p.37Chapter 2.7 --- A Necessary and Sufficient Condition --- p.42Chapter 3 --- Redundancy of Optimal Fix-Free Codes --- p.44Chapter 3.1 --- Introduction --- p.44Chapter 3.2 --- An Upper Bound in Terms of q --- p.46Chapter 3.3 --- An Upper Bound in Terms of p1 --- p.48Chapter 3.4 --- An Upper Bound in Terms of pn --- p.51Chapter 4 --- Two Applications of the Probabilistic Method --- p.54Chapter 4.1 --- An Alternative Proof for the Kraft Inequality --- p.54Chapter 4.2 --- A Characteristic Inequality for ´ب1´ة-ended Codes --- p.59Chapter 5 --- Summary and Future Work --- p.69Appendix --- p.71A Length Assignment for Upper Bounding the Redundancy of Fix-Free Codes --- p.71Bibliography --- p.7

Content-aware compression for big textual data analysis

A substantial amount of information on the Internet is present in the form of text. The value of this semi-structured and unstructured data has been widely acknowledged, with consequent scientific and commercial exploitation. The ever-increasing data production, however, pushes data analytic platforms to their limit. This thesis proposes techniques for more efficient textual big data analysis suitable for the Hadoop analytic platform. This research explores the direct processing of compressed textual data. The focus is on developing novel compression methods with a number of desirable properties to support text-based big data analysis in distributed environments. The novel contributions of this work include the following. Firstly, a Content-aware Partial Compression (CaPC) scheme is developed. CaPC makes a distinction between informational and functional content in which only the informational content is compressed. Thus, the compressed data is made transparent to existing software libraries which often rely on functional content to work. Secondly, a context-free bit-oriented compression scheme (Approximated Huffman Compression) based on the Huffman algorithm is developed. This uses a hybrid data structure that allows pattern searching in compressed data in linear time. Thirdly, several modern compression schemes have been extended so that the compressed data can be safely split with respect to logical data records in distributed file systems. Furthermore, an innovative two layer compression architecture is used, in which each compression layer is appropriate for the corresponding stage of data processing. Peripheral libraries are developed that seamlessly link the proposed compression schemes to existing analytic platforms and computational frameworks, and also make the use of the compressed data transparent to developers. The compression schemes have been evaluated for a number of standard MapReduce analysis tasks using a collection of real-world datasets. In comparison with existing solutions, they have shown substantial improvement in performance and significant reduction in system resource requirements

Codes robustes et codes joints source-canal pour transmission multimédia sur canaux mobiles

Some new error-resilient source coding and joint source/channel coding techniquesare proposed for the transmission of multimedia sources over error-prone channels.First, we introduce a class of entropy codes providing unequal error-resilience, i.e.providing some protection to the most sensitive information. These codes are thenextended to exploit the temporal dependencies. A new state model based on the aggregation of some states of the trellis is thenproposed and analyzed for soft source decoding of variable length codes with a lengthconstraint. It allows the weighting of the compromise between the estimation accuracyand the decoding complexity.Next, some paquetization methods are proposed to reduce the error propagationphenomenon of variable length codes.Finally, some re-writing rules are proposed to extend the binary codetree representationof entropy codes. The proposed representation allows in particular the designof codes with improved soft decoding performances.Cette thèse propose des codes robustes et des codes conjoints source/canal pourtransmettre des signaux multimédia sur des canaux bruités. Nous proposons des codesentropiques offrant une résistance intrinsèque aux données prioritaires. Ces codes sontétendus pour exploiter la dépendance temporelle du signal.Un nouveau modèle d’état est ensuite proposé et analysé pour le décodage souplede codes à longueur variable avec une contrainte de longueur. Il permet de réglerfinement le compromis performance de décodage/complexité.Nous proposons également de séparer, au niveau du codage entropique, les étapesde production des mots de codes et de paquétisation. Différentes stratégies de constructionde train binaire sont alors proposées.Enfin, la représentation en arbre binaire des codes entropiques est étendue enconsidérant des règles de ré-écriture. Cela permet en particulier d’obtenir des codesqui offrent des meilleures performances en décodage souple