相关论文: Structural Properties of Index Coding Capacity Usi…

The index coding problem studies the fundamental limit on broadcasting multiple messages to their respective receivers with different sets of side information that are represented by a directed graph. The generalized lexicographic product…

A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding,…

We propose a novel technique for constructing a graph representation of a code through which we establish a significant connection between the service rate problem and the well-known fractional matching problem. Using this connection, we…

The storage capacity of a graph measures the maximum amount of information that can be stored across its vertices, such that the information at any vertex can be recovered from the information stored at its neighborhood. The study of this…

The question of under what condition some side information for index coding can be removed without affecting the capacity region is studied, which was originally posed by Tahmasbi, Shahrasbi, and Gohari. To answer this question, the notion…

In index coding, a server broadcasts multiple messages to their respective receivers, each with some side information that can be utilized to reduce the amount of communication from the server. Distributed index coding is an extension of…

Three science and engineering problems of recent interests -index coding, locally recoverable distributed storage, and guessing games on graphs- are discussed and the connection between their optimal solutions is elucidated. By generalizing…

Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…

The distributed index coding problem is studied, whereby multiple messages are stored at different servers to be broadcast to receivers with side information. First, the existing composite coding scheme is enhanced for the centralized…

We suggest an enhancement to structural coding through the use of (a) causally bound codes, (b) basic constructs of graph theory and (c) statistics. As is the norm with structural coding, the codes are collected into categories. The…

Index coding and coded caching are two active research topics in information theory with strong ties to each other. Motivated by the multi-access coded caching problem, we study a new class of structured index coding problems (ICPs) which…

One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…

One of the main theoretical motivations for the emerging area of network coding is the achievability of the max-flow/min-cut rate for single source multicast. This can exceed the rate achievable with routing alone, and is achievable with…

The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general…

In this paper, we study the capacity region of the general distributed index coding. In contrast to the traditional centralized index coding where a single server contains all $n$ messages requested by the receivers, in the distributed…

The routing capacity region of networks with multiple unicast sessions can be characterized using Farkas' lemma as an infinite set of linear inequalities. In this paper this result is sharpened by exploiting properties of the solution…

Motivated by applications in distributed storage, the storage capacity of a graph was recently defined to be the maximum amount of information that can be stored across the vertices of a graph such that the information at any vertex can be…

Color coding is an algorithmic technique used in parameterized complexity theory to detect "small" structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable,…

Studying the energy partioning published in nucl-th/0406056v2 we show that the presented results do not fulfill the sum rule due to energy conservation. The observed fluctuations of the energy conservation test point to a numerical problem.…

Explicit characterization and computation of the multi-source network coding capacity region (or even bounds) is long standing open problem. In fact, finding the capacity region requires determination of the set of all entropic vectors…