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

Decentralized Erasure Codes for Distributed Networked Storage

We consider the problem of constructing an erasure code for storage over a network when the data sources are distributed. Specifically, we assume that there are n storage nodes with limited memory and k<n sources generating the data. We want a data collector, who can appear anywhere in the network, to query any k storage nodes and be able to retrieve the data. We introduce Decentralized Erasure Codes, which are linear codes with a specific randomized structure inspired by network coding on random bipartite graphs. We show that decentralized erasure codes are optimally sparse, and lead to reduced communication, storage and computation cost over random linear coding.Comment: to appear in IEEE Transactions on Information Theory, Special Issue: Networking and Information Theor

An information-theoretic view of network management

We present an information-theoretic framework for network management for recovery from nonergodic link failures. Building on recent work in the field of network coding, we describe the input-output relations of network nodes in terms of network codes. This very general concept of network behavior as a code provides a way to quantify essential management information as that needed to switch among different codes (behaviors) for different failure scenarios. We compare two types of recovery schemes, receiver-based and network-wide, and consider two formulations for quantifying network management. The first is a centralized formulation where network behavior is described by an overall code determining the behavior of every node, and the management requirement is taken as the logarithm of the number of such codes that the network may switch among. For this formulation, we give bounds, many of which are tight, on management requirements for various network connection problems in terms of basic parameters such as the number of source processes and the number of links in a minimum source-receiver cut. Our results include a lower bound for arbitrary connections and an upper bound for multitransmitter multicast connections, for linear receiver-based and network-wide recovery from all single link failures. The second is a node-based formulation where the management requirement is taken as the sum over all nodes of the logarithm of the number of different behaviors for each node. We show that the minimum node-based requirement for failures of links adjacent to a single receiver is achieved with receiver-based schemes

All-Optical Network Coding

In this paper, we investigate the application of network coding to all-optical networks from both the algorithmic and infrastructural perspectives. We study the effectiveness of using network coding for optical-layer dedicated protection of multicast traffic which provides robustness against link failures in the network. We present a heuristic for solving this problem and compare it with both inefficient optimal methods and non-network coding approaches. Our experiments show that our heuristic provides near optimal performance while significantly outperforming existing approaches for dedicated multicast protection. We also propose architectures for specialized all-optical circuits capable of performing the processing required for network coding and show how these devices can be effectively deployed in an all-optical multicast network

Network Coding for WDM All-Optical Multicast

Network coding has become a useful means for achieving efficient multicast, and the optical community has started to examine its application to optical networks. However, a number of challenges, including limited processing capability and coarse bandwidth granularity, need to be overcome before network coding can be effectively used in optical networks. In this paper, we address some of these problems. We consider the problem of finding efficient routes to use with coding, and we study the effectiveness of using network coding for optical-layer dedicated protection of multicast traffic. We also propose architectures for all-optical circuits capable of performing the processing required for network coding. Our experiments show that network coding provides a moderate improvement in bandwidth efficiency for unprotected multicast while significantly outperforming existing approaches for dedicated multicast protection