Related papers: Generalized Index Coding Problem and Discrete Poly…
The connection between index coding and matroid theory have been well studied in the recent past. El Rouayheb et al. established a connection between multi linear representation of matroids and wireless index coding. Muralidharan and Rajan…
Discrete polymatroids are the multi-set analogue of matroids. In this paper, we explore the connections among linear network coding, linear index coding and representable discrete polymatroids. We consider vector linear solutions of…
The connection between index coding and matroid theory have been well studied in the recent past. El Rouayheb et al. established a connection between multilinear representation of matroids and wireless index coding. Muralidharan and Rajan…
The \emph{index coding} problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad-hoc networks. An instance of the index coding problem includes a…
An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding…
An index coding (IC) problem consisting of a server and multiple receivers with different side-information and demand sets can be equivalently represented using a fitting matrix. A scalar linear index code to a given IC problem is a matrix…
The index coding problem is studied from an interference alignment perspective, providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between multiple unicast…
In this paper, a general algorithm is proposed for rate analysis and code design of linear index coding problems. Specifically a solution for minimum rank matrix completion problem over finite fields representing the linear index coding…
We study index-coding problems (one sender broadcasting messages to multiple receivers) where each message is requested by one receiver, and each receiver may know some messages a priori. This type of index-coding problems can be fully…
The groupcast index coding problem is the most general version of the classical index coding problem, where any receiver can demand messages that are also demanded by other receivers. Any groupcast index coding problem is described by its…
We study the fundamental problem of index coding under an additional privacy constraint that requires each receiver to learn nothing more about the collection of messages beyond its demanded messages from the server and what is available to…
In this paper we show that the Index Coding problem captures several important properties of the more general Network Coding problem. An instance of the Index Coding problem includes a server that holds a set of information messages…
It has been known that the insufficiency of linear coding in achieving the optimal rate of the general index coding problem is rooted in its rate's dependency on the field size. However, this dependency has been described only through the…
A linear Fractional Network Coding (FNC) solution over $\mathbb{F}_q$ is a linear network coding solution over $\mathbb{F}_q$ in which the message dimensions need not necessarily be the same and need not be the same as the edge vector…
The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer…
We consider the following \textit{network computation problem}. In an acyclic network, there are multiple source nodes, each generating multiple messages, and there are multiple sink nodes, each demanding a function of the source messages.…
This letter investigates a new class of index coding problems. One sender broadcasts packets to multiple users, each desiring a subset, by exploiting prior knowledge of linear combinations of packets. We refer to this class of problems as…
This paper considers a base station that delivers packets to multiple receivers through a sequence of coded transmissions. All receivers overhear the same transmissions. Each receiver may already have some of the packets as side…
Index coding is concerned with efficient broadcast of a set of messages to receivers in the presence of receiver side information. In this paper, we study the secure index coding problem with security constraints on the receivers…
In Index coding there is a single sender with multiple messages and multiple receivers each wanting a different set of messages and knowing a different set of messages a priori. The Index Coding problem is to identify the minimum number of…