Polynomial time algorithms for multicast network code construction

The famous max-flow min-cut theorem states that a source node s can send information through a network (V, E) to a sink node t at a rate determined by the min-cut separating s and t. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to re-encode the information they receive. We demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed. We give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity. We extend these algorithms to integer capacities and to codes that are tolerant to edge failures

Network Coding for Multi-Resolution Multicast

Multi-resolution codes enable multicast at different rates to different receivers, a setup that is often desirable for graphics or video streaming. We propose a simple, distributed, two-stage message passing algorithm to generate network codes for single-source multicast of multi-resolution codes. The goal of this "pushback algorithm" is to maximize the total rate achieved by all receivers, while guaranteeing decodability of the base layer at each receiver. By conducting pushback and code generation stages, this algorithm takes advantage of inter-layer as well as intra-layer coding. Numerical simulations show that in terms of total rate achieved, the pushback algorithm outperforms routing and intra-layer coding schemes, even with codeword sizes as small as 10 bits. In addition, the performance gap widens as the number of receivers and the number of nodes in the network increases. We also observe that naiive inter-layer coding schemes may perform worse than intra-layer schemes under certain network conditions.Comment: 9 pages, 16 figures, submitted to IEEE INFOCOM 201

Multiple-Tree Push-based Overlay Streaming

Multiple-Tree Overlay Streaming has attracted a great amount of attention from researchers in the past years. Multiple-tree streaming is a promising alternative to single-tree streaming in terms of node dynamics and load balancing, among others, which in turn addresses the perceived video quality by the streaming user on node dynamics or when heterogeneous nodes join the network. This article presents a comprehensive survey of the different aproaches and techniques used in this research area. In this paper we identify node-disjointness as the property most approaches aim to achieve. We also present an alternative technique which does not try to achieve this but does local optimizations aiming global optimizations. Thus, we identify this property as not being absolute necessary for creating robust and heterogeneous multi-tree overlays. We identify two main design goals: robustness and support for heterogeneity, and classify existing approaches into these categories as their main focus

Minimum cost mirror sites using network coding: Replication vs. coding at the source nodes

Content distribution over networks is often achieved by using mirror sites that hold copies of files or portions thereof to avoid congestion and delay issues arising from excessive demands to a single location. Accordingly, there are distributed storage solutions that divide the file into pieces and place copies of the pieces (replication) or coded versions of the pieces (coding) at multiple source nodes. We consider a network which uses network coding for multicasting the file. There is a set of source nodes that contains either subsets or coded versions of the pieces of the file. The cost of a given storage solution is defined as the sum of the storage cost and the cost of the flows required to support the multicast. Our interest is in finding the storage capacities and flows at minimum combined cost. We formulate the corresponding optimization problems by using the theory of information measures. In particular, we show that when there are two source nodes, there is no loss in considering subset sources. For three source nodes, we derive a tight upper bound on the cost gap between the coded and uncoded cases. We also present algorithms for determining the content of the source nodes.Comment: IEEE Trans. on Information Theory (to appear), 201

On robust network coding subgraph construction under uncertainty

We consider the problem of network coding subgraph construction in networks where there is uncertainty about link loss rates. For a given set of scenarios specified by an uncertainty set of link loss rates, we provide a robust optimization-based formulation to construct a single subgraph that would work relatively well across all scenarios. We show that this problem is coNP-hard in general for both objectives: minimizing cost of subgraph construction and maximizing throughput given a cost constraint. To solve the problem tractably, we approximate the problem by introducing path constraints, which results in polynomial time-solvable solution in terms of the problem size. The simulation results show that the robust optimization solution is better and more stable than the deterministic solution in terms of worst-case performance. From these results, we compare the tractability of robust network design problems with different uncertain network components and different problem formulations