Dynamic index coding for wireless broadcast networks

Abstract

Abstract-We consider a wireless broadcast station that transmits packets to multiple users. The packet requests for each user may overlap, and some users may already have certain packets. This presents a problem of broadcasting in the presence of side information, and is a generalization of the well known (and unsolved) index coding problem of information theory. Rather than achieving the full capacity region, we develop a code-constrained capacity region, which restricts attention to a pre-specified set of coding actions. We develop a dynamic maxweight algorithm that allows for random packet arrivals and supports any traffic inside the code-constrained capacity region. Further, we provide a simple set of codes based on cycles in the underlying demand graph. We show these codes are optimal for a class of broadcast relay problems.

Bipartite Index coding Protocol

“…In their work, an instance of an index coding problem is represented by a directed graph, where one vertex (node) represents a requested packet and a directed edge P k i ,P l j indicates that U i has packet P l j and needs packet P k i . On this graph, the NP-hard minimum cycle cover must be found [11], [12]. The directed graph approach is restricted to problems where no packet is demanded by more than one user.…”

Dynamic index coding gain over a complete bi-directional side information graph

“…This minimum required bits is called the optimal index code length. This problem can be represented by a directed bipartite graph [1] or a hypergraph [2]. In case that the receivers need distinct messages, the index coding problem could be represented by a directed graph in which the vertex is connected to the vertex by a directed edge or equivalently ( , ) ∈ , is the set of edges, if ∈ .…”

“…In the first side, the researchers try to find the optimal index code length. Using graph and information theoretic approaches, several upper and lower bounds for the optimal index code length ℓ * ( ) are obtained [1]- [10]. In [4], [11], they show that the optimal linear index code is equal to a graph parameter called min-rank.…”

“…In the second side, the generalization of the conventional index coding problem scenario is considered [1], [15], [16]. In our paper, which fits in this direction, we consider the problem of dynamic index coding introduced in [1] which is a more practical and complex version of the index coding problem dealing with random traffics instead of a fixed batch of packets.…”

Finding three transmissions is hard

“…The most general representation of the problem is offered in [14], [15] where an instance of the problem is represented by a bipartite graph. In this more general problem, each bit can be demanded by more than one user and the number of bits and users need not be equal.…”