Graph-Theoretical Constructions for Graph Entropy and Network Coding Based Communications
نویسندگان
چکیده
منابع مشابه
Graph Entropy, Network Coding and Guessing games
We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below with the number of vertices minus the size of the graph’s shortest index code. We show that the Network Coding solvability of each specific multiple unicast n...
متن کاملGraph Connectivity and Network Coding
Graph Connectivity and Network Coding LEUNG, Kai Man Master of Philosophy Department of Computer Science and Engineering The Chinese University of Hong Kong 2011 In this thesis we present a new algebraic formulation to compute edge connectivities in a directed graph, using the ideas developed in network coding. This reduces the problem of computing edge connectivities to solving systems of line...
متن کاملGraph-based Codes and Generalized Product Constructions
Fountain codes are a class of rateless codes well-suited for communication over erasure channels with unknown erasure parameter. We analyze the decoding of LT codes, the first instance of practical, universal Fountain codes. A set of interest during LT decoding is the set of output symbols of reduced degree one (the “ripple”). The evolution of the ripple size throughout the decoding process is ...
متن کاملThe Graph-Theoretical Properties of Partitions and Information Entropy
The information entropy, as a measurement of the average amount of information contained in an information system, is used in the classification of objects and the analysis of information systems. The information entropy of a partition is non-increasing when the partition is refined, and is related to rough sets by Wong and Ziarko. The partitions and information entropy have some graph-theoreti...
متن کاملGraph properties, graph limits, and entropy
We study the relation between the growth rate of a graph property and the entropy of the graph limits that arise from graphs with that property. In particular, for hereditary classes we obtain a new description of the colouring number, which by well-known results describes the rate of growth. We study also random graphs and their entropies. We show, for example, that if a hereditary property ha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2011
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2011.2155618