Multilevel Diversity Coding with Secure Regeneration: Separate Coding Achieves the MBR Point

The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer bounds are established, showing that separate coding of different messages using the respective SRCs can achieve the minimum-bandwidth-regeneration (MBR) point of the achievable normalized storage-capacity repair-bandwidth tradeoff regions for the general MDC-SR problem. The core of the new converse results is an exchange lemma, which can be established using Han's subset inequality

Weakly Secure Symmetric Multilevel Diversity Coding

Multilevel diversity coding is a classical coding model where multiple mutually independent information messages are encoded, such that different reliability requirements can be afforded to different messages. It is well known that {\em superposition coding}, namely separately encoding the independent messages, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). In the current paper, we consider weakly secure SMDC where security constraints are injected on each individual message, and provide a complete characterization of the conditions under which superposition coding is sum-rate optimal. Two joint coding strategies, which lead to rate savings compared to superposition coding, are proposed, where some coding components for one message can be used as the encryption key for another. By applying different variants of Han's inequality, we show that the lack of opportunity to apply these two coding strategies directly implies the optimality of superposition coding. It is further shown that under a set of particular security constraints, one of the proposed joint coding strategies can be used to construct a code that achieves the optimal rate region.Comment: The paper has been accepted by IEEE Transactions on Information Theor

The Explicit Coding Rate Region of Symmetric Multilevel Diversity Coding

It is well known that {\em superposition coding}, namely separately encoding the independent sources, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). However, the characterization of the coding rate region therein involves uncountably many linear inequalities and the constant term (i.e., the lower bound) in each inequality is given in terms of the solution of a linear optimization problem. Thus this implicit characterization of the coding rate region does not enable the determination of the achievability of a given rate tuple. In this paper, we first obtain closed-form expressions of these uncountably many inequalities. Then we identify a finite subset of inequalities that is sufficient for characterizing the coding rate region. This gives an explicit characterization of the coding rate region. We further show by the symmetry of the problem that only a much smaller subset of this finite set of inequalities needs to be verified in determining the achievability of a given rate tuple. Yet, the cardinality of this smaller set grows at least exponentially fast with $L$. We also present a subset entropy inequality, which together with our explicit characterization of the coding rate region, is sufficient for proving the optimality of superposition coding

Content analysing multi-level authority and cultural identity claims: a complement to the Comparative Manifestos Project (CMP) exemplified for Spanish regional manifestos

"This handbook describes a specific approach to content analyzing multilevel party manifestos, building on a methodology that was originally developed in the context of the Manifesto Research Group (MRG). Since 1979, the MRG has been collecting and coding election programs with the aim of estimating policy preferences of political parties. The second phase of the project started in 1989. In the context of its 'Comparative Manifestos Project' (CMP), the Social Science Research Center Berlin (WZB) provided resources for updating and expanding the MRG data. Since then, country experts were hired to collect and code national election programs according to a handbook that describes how to identify the coding units and how to apply the classification scheme of policy preferences under central supervision. The CMP is solely concerned with national election programs. However, in decentralized political systems, parties also publish local and regional election programs and, in times of globalization, transnational party federations increasingly produce joint programs. Comparing these multilevel manifestos can provide additional answers to questions of multilevel governance. This handbook, elaborated in collaboration with the Instituto de Estudios Sociales Avanzados de Andalucía (IESA-CSIC, Spain), presents a classical content analytical approach to identifying parties' multilevel preferences. It instructs coders on how to apply two combined content analytical classification schemes: first, the CMP classification of policy preferences developed for party manifestos at national levels and, second, a classification of cultural and authority claims on multiple levels of governance. This double classification scheme is then applied to regional party manifestos in Spain, providing examples of multilevel analysis for training coders and testing their grasp of the complex concepts of parties' multilevel preferences." (author's abstract)"Der vorliegende Ansatz zur Inhaltsanalyse von Parteiprogrammen in politischen Mehrebenensystemen basiert auf einer Methodologie, die im Rahmen der Manifesto Research Group (MRG) entwickelt wurde. 1979 begann die MRG Parteiprogramme zu sammeln und zu analysieren, um politische Positionen von Parteien komparativ anhand eines klassischen inhaltanalytischen Ansatzes zu messen. Seit 1989 stellte das Wissenschaftszentrum Berlin für Sozialforschung (WZB) im Rahmen des 'Comparative Manifestos Projects' (CMP) Mittel zur Verfügung, um die Daten der MRG zu aktualisieren und zu erweitern. Seither werden Länderexperten damit beauftragt, die Wahlprogramme unter zentraler Begleitung und Kontrolle zu kodieren. Dabei erläutert ein Handbuch die Identifikation der Kodiereinheiten und die Anwendung des Klassifikationsschemas der politischen Positionen. Das CMP befasst sich ausschließlich mit Parteiprogrammen zu nationalen Wahlen. In dezentralisierten politischen Systemen geben Parteien aber auch lokale und regionale Wahlprogramme heraus; transnationale Parteienzusammenschlüsse verfassen in Zeiten der Globalisierung zunehmend gemeinsame Programme. Ein Vergleich solcher Programme für verschiedene Ebenen kann neue Einsichten in Governanceprobleme von Mehrebenensystemen ermöglichen. Dieses Handbuch wurde in Zusammenarbeit mit dem spanischen Instituto de Estudios Sociales Avanzados de Andalucía (IESA-CSIC) zur Identifikation von Parteienpositionen in Mehrebenensystemen verfasst. Es beschreibt, wie Coder zwei inhaltsanalytische Klassifikationsschemata anwenden können, die miteinander kombiniert sind: einerseits die CMP-Klassifikation politischer Positionen und andererseits eine Klassifikation von kulturellen und politischen Autonomieansprüchen auf verschiedenen Ebenen von Governance. Diese doppelte Klassifikation wird auf spanische Regionalwahlprogramme angewendet. Beispiele spanischer Regionalprogramme dienen auch der Ausbildung von Codern und der Überprüfung ihres Verständnisses der komplexen Konzepte von Parteipositionen in Mehrebenensystemen." (Autorenreferat

Fundamental Limits of Exact-Repair Regenerating Codes

Understanding the fundamental limits of communication systems involves both constructing efficient coding schemes as well as proving mathematically that certain performance is impossible to achieve; the latter is known as the converse problem in information theory. This thesis focused on the converse problems for complex information systems such as self-repair distributed storage and coded caching systems, and our goal was to establish tight converse results for such systems by exploiting problem-specific combinatorial structures. The main part of this thesis dealt with exact-repair regenerating codes, which were first proposed by Dimakis et al. in 2010. In particular, we considered two extensions of the original setting of Dimakis et al., namely 1) multilevel diversity coding with regeneration and 2) secure exact-repair regenerating codes. For the problem of multilevel diversity coding with regeneration, we showed, via the proposed combinatorial approach, that the natural separate encoding strategy can achieve the optimal tradeoff between the normalized storage capacity and repair bandwidth at the minimum-bandwidth rate (MBR) point. This settled a conjecture by Tian and Liu in 2015. For the problem of secure exact-repair regenerating codes, all known results from the literature showed that the achievable tradeoff regions between the normalized storage capacity and repair bandwidth have a single corner point, achieved by a scheme proposed by Shah, Rashmi and Kumar (the SRK point). Since the achievable tradeoff regions of the exact-repair regenerating code problem without any secrecy constraints were known to have multiple corner points in general, these existing results suggested a phase-change-like behavior, i.e., enforcing a secrecy constraint immediately reduces the tradeoff region to one with a single corner point. In our work, we first showed that when the secrecy parameter is sufficiently large, the SRK point is indeed the only corner point of the tradeoff region. However, when the secrecy parameter is small, we showed that the tradeoff region can, in fact, have multiple corner points. In particular, we established a precise characterization of the tradeoff region for a particular problem instance, which has exactly two corner points. Thus, a smooth transition, instead of a phase-change-type of transition, should be expected as the secrecy constraint is gradually strengthened