S. M. Sadegh Tabatabaei Yazdi

A combinatorial study of linear deterministic relay networks

The linear deterministic network model of Avestimehr, Diggavi and Tse has attracted attention because it captures certain physical aspects of wireless communication such as broadcasting and interference but is discrete and deterministic like traditional wireline network models. We study the unicast problem for this network model using results from matroid theory and submodular optimization, and we provide deterministic and polynomial-time coding schemes that can achieve the capacity.

Network Coding in Node-Constrained Line and Star Networks

Line and star networks with both node and edge constraints are studied in the network coding framework. For line networks, the capacity region of the general multiple multicast problem is established. The coding theorem is based on a binary linear coding scheme, while the converse requires new upper bounds that improve on standard cut-based bounds. For star networks, the multiple unicast problem is examined. Capacity upper bounds are derived and a simple linear coding scheme is proposed which is based on the combinatorial optimization problem of cycle packing in directed graphs. The optimality of this scheme is established for a broad class of demands. The connection of node-constrained network coding in star networks, and index coding with side information is discussed and used to partially characterize the optimal linear code for general rates.

A Max-Flow/Min-Cut Algorithm for Linear Deterministic Relay Networks

The linear deterministic model of relay networks (LDRN) is a generalization of the traditional directed network model which has become popular in the study of the flow of information over wireless communication networks. The max-flow/min-cut theorem for a multicast session over a directed network has been extended to this wireless relay model. The result was first proved by a random coding scheme over large blocks of transmitted signals. In this paper, in the special case of a unicast session, a simple capacity-achieving transmission scheme for LDRN which codes over one symbol of information at each use of the network is obtained by a connection to the submodular flow problem and through the application of tools from matroid theory and submodular optimization theory. Polynomial-time algorithms for calculating the capacity of the network and the optimal coding scheme are implied by our analysis.

A deterministic polynomialtime algorithm for constructing a multicast coding scheme for linear deterministic relay networks

We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the well-known multicast network coding scheme of Jaggi to linear deterministic relay networks and is based on the notion of flow for a unicast session that was introduced by the authors in earlier work. We present randomized and deterministic polynomial-time versions of our algorithm and show that for a network with g destinations, our deterministic algorithm can achieve the capacity in [log(g+1)] uses of the network and has the fastest construction time among algorithms for this problem.

A Deterministic Polynomial-Time Algorithm for Constructing a Multicast Coding Scheme for Linear Deterministic Relay Networks

We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the well-known multicast network coding scheme of Jaggi to linear deterministic relay networks and is based on the notion of flow for a unicast session that was introduced by the authors in earlier work. We present randomized and deterministic polynomial-time versions of our algorithm and show that for a network with g destinations, our deterministic algorithm can achieve the capacity in [log(g+1)] uses of the network and has the fastest construction time among algorithms for this problem.

Network coding on line networks with broadcast

An achievable rate region for line networks with edge and node capacity constraints and broadcasting is derived. The region is the capacity region if the broadcast channels are orthogonal or physically degraded.

On describing the routing capacity regions of networks

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 satisfied by each rate-tuple on the boundary of the capacity region, and a finite description of the routing capacity region which depends on network parameters is offered. For the special case of undirected ring networks additional results on the complexity of the description are provided.