A Network Coding Approach to Loss Tomography

Network tomography aims at inferring internal network characteristics based on measurements at the edge of the network. In loss tomography, in particular, the characteristic of interest is the loss rate of individual links and multicast and/or unicast end-to-end probes are typically used. Independently, recent advances in network coding have shown that there are advantages from allowing intermediate nodes to process and combine, in addition to just forward, packets. In this paper, we study the problem of loss tomography in networks with network coding capabilities. We design a framework for estimating link loss rates, which leverages network coding capabilities, and we show that it improves several aspects of tomography including the identifiability of links, the trade-off between estimation accuracy and bandwidth efficiency, and the complexity of probe path selection. We discuss the cases of inferring link loss rates in a tree topology and in a general topology. In the latter case, the benefits of our approach are even more pronounced compared to standard techniques, but we also face novel challenges, such as dealing with cycles and multiple paths between sources and receivers. Overall, this work makes the connection between active network tomography and network coding

Active Learning of Multiple Source Multiple Destination Topologies

We consider the problem of inferring the topology of a network with $M$ sources and $N$ receivers (hereafter referred to as an $M$-by-$N$ network), by sending probes between the sources and receivers. Prior work has shown that this problem can be decomposed into two parts: first, infer smaller subnetwork components (i.e., $1$-by-$N$'s or $2$-by-$2$'s) and then merge these components to identify the $M$-by-$N$ topology. In this paper, we focus on the second part, which had previously received less attention in the literature. In particular, we assume that a $1$-by-$N$ topology is given and that all $2$-by-$2$ components can be queried and learned using end-to-end probes. The problem is which $2$-by-$2$'s to query and how to merge them with the given $1$-by-$N$, so as to exactly identify the $2$-by-$N$ topology, and optimize a number of performance metrics, including the number of queries (which directly translates into measurement bandwidth), time complexity, and memory usage. We provide a lower bound, $\lceil \frac{N}{2} \rceil$, on the number of $2$-by-$2$'s required by any active learning algorithm and propose two greedy algorithms. The first algorithm follows the framework of multiple hypothesis testing, in particular Generalized Binary Search (GBS), since our problem is one of active learning, from $2$-by-$2$ queries. The second algorithm is called the Receiver Elimination Algorithm (REA) and follows a bottom-up approach: at every step, it selects two receivers, queries the corresponding $2$-by-$2$, and merges it with the given $1$-by-$N$; it requires exactly $N-1$ steps, which is much less than all $\binom{N}{2}$ possible $2$-by-$2$'s. Simulation results over synthetic and realistic topologies demonstrate that both algorithms correctly identify the $2$-by-$N$ topology and are near-optimal, but REA is more efficient in practice

Multiple source multiple destination topology inference using network coding

n this paper, we combine network cod- ing and tomographic techniques for topology infer- ence. Our goal is to infer the topology of a network by sending probes between a given set of multiple sources and multiple receivers and by having interme- diate nodes perform network coding operations. We combine and extend two ideas that have been devel- oped independently. On one hand, network coding introduces topology-dependent correlation, which can then be exploited at the receivers to infer the topology [1]. On the other hand, it has been shown that a tradi- tional (i.e., without network coding) multiple source, multiple receiver tomography problem can be decom- posed into multiple two source, two receiver subprob- lems [2]. Our first contribution is to show that, when intermediate nodes perform network coding, topolog- ical information contained in network coded packets allows to accurately distinguish among all different 2- by-2 subnetwork components, which was not possible with traditional tomographic techniques. Our second contribution is to use this knowledge to merge the subnetworks and accurately reconstruct the general topology. Our approach is applicable to any general Internet-like topology, and is robust to the presence of delay variability and packet loss

Active topology inference using network coding

Our goal, in this paper, is to infer the topology of a network when (i) we can send probes between sources and receivers at the edge of the network and (ii) intermediate nodes can perform simple network coding operations, i.e., additions. Our key intuition is that network coding introduces topology-dependent correlation in the observations at the receivers, which can be exploited to infer the topology. For undirected tree topologies, we design hierarchical clustering algorithms, building on our prior work in [24]. For directed acyclic graphs (DAGs), first we decompose the topology into a number of two source, two receiver (2-by-2) subnetwork components and then we merge these components to reconstruct the topology. Our approach for DAGs builds on prior work on tomography [36], and improves upon it by employing network coding to accurately distinguish among all different 2-by-2 components. We evaluate our algorithms through simulation of a number of realistic topologies and compare them to active tomographic techniques without network coding. We also make connections between our approach and other alternatives, including passive inference, traceroute, and packet marking

Maximum likelihood estimation for multiple-source losss tomography with network coding

Loss tomography aims at inferring the loss rate of links in a network from end-to-end measurements. Previous work in [1] has developed optimal maximum likelihood estimators (MLEs) for link loss rates in a single-source multicast tree. However, only sub-optimal algorithms have been developed for multiple-source loss tomography [2]–[5]. In this paper, we revisit multiple-source loss tomography in tree networks with multicast and network coding capabilities, and we provide, for the first time, low-complexity MLEs for the link loss rates. We also derive the rate of convergence of the estimators

A network coding approach to IP traceback

Abstract—Traceback schemes aim at identifying the source(s) of a sequence of packets and the nodes these packets traversed. This is useful for tracing the sources of high volume traffic, e.g., in Distributed Denial-of-Service (DDoS) attacks. In this paper, we are particularly interested in Probabilistic Packet Marking (PPM) schemes, where intermediate nodes probabilistically mark packets with information about their identity and the receiver uses information from several packets to reconstruct the paths they have traversed. Our work is inspired by two observations. First, PPM is essentially a coupon collector’s problem [1], [2]. Second, the coupon collector’s problem significantly benefits from network coding ideas [3], [4]. Based on these observations, we propose a network coding-based approach (PPM+NC) that marks packets with random linear combinations of router IDs, instead of individual router IDs. We demonstrate its benefits through analysis. We then propose a practical PPM+NC scheme based on the main PPM+NC idea, but also taking into account the limited bit budget in the IP header available for marking and other practical constraints. Simulation results show that our scheme significantly reduces the number of packets needed to reconstruct the attack graph, in both single- and multi-path scenarios, thus increasing the speed of tracing the attack back to its source(s). I

Multiple source multiple destination topology inference using network coding

Abstract — In this paper, we combine network coding and tomographic techniques for topology inference. Our goal is to infer the topology of a network by sending probes between a given set of multiple sources and multiple receivers and by having intermediate nodes perform network coding operations. We combine and extend two ideas that have been developed independently. On one hand, network coding introduces topology-dependent correlation, which can then be exploited at the receivers to infer the topology [1]. On the other hand, it has been shown that a traditional (i.e., without network coding) multiple source, multiple receiver tomography problem can be decomposed into multiple two source, two receiver subproblems [2]. Our first contribution is to show that, when intermediate nodes perform network coding, topological information contained in network coded packets allows to accurately distinguish among all different 2-by-2 subnetwork components, which was not possible with traditional tomographic techniques. Our second contribution is to use this knowledge to merge the subnetworks and accurately reconstruct the general topology. Our approach is applicable to any general Internet-like topology, and is robust to the presence of delay variability and packet loss. I