This paper describes MIXIT, a system that improves the throughput of wireless mesh networks. MIXIT exploits a basic property of mesh networks: even when no node receives a packet correctly, any given bit is likely to be received by some node correctly. Instead of insisting on forwarding only correct packets, MIXIT routers use physical layer hints to make their best guess about which bits in a corrupted packet are likely to be correct and forward them to the destination. Even though this approach inevitably lets erroneous bits through, we find that it can achieve high throughput without compromising end-to-end reliability. The core component of MIXIT is a novel network code that operates on small groups of bits, called symbols. It allows the nodes to opportunistically route groups of bits to their destination with low overhead. MIXIT’s network code also incorporates an end-to-end error correction component that the destination uses to correct any errors that might seep through. We have implemented MIXIT on a software radio platform running the Zigbee radio protocol. Our experiments on a 25-node indoor testbed show that MIXIT has a throughput gain of 2.8 × over MORE, a state-of-the-art opportunistic routing scheme, and about 3.9 × over traditional routing using the ETX metric.

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Recent studies show that network coding can provide significant benefits to network protocols, such as increased throughput, reduced network congestion, higher reliability, and lower power consumption. The core principle of network coding is that intermediate nodes actively mix input packets to produce output packets. This mixing subjects network coding systems to a severe security threat, known as a pollution attack, where attacker nodes inject corrupted packets into the network. Corrupted packets propagate in an epidemic manner, depleting network resources and significantly decreasing throughput. Pollution attacks are particularly dangerous in wireless networks, where attackers can easily inject packets or compromise devices due to the increased network vulnerability. In this paper, we address pollution attacks against network coding systems in wireless mesh networks. We demonstrate that previous

Abstract — In this paper, we present new results on network error correction with unequal link capacities. We consider network error correction codes that can correct arbitrary errors occurring on up to z links. We find the capacity of a two-node network with multiple feedback links and show how feedback links can be used to increase the error correction capacity. We propose a new cut-set upper bound for general acyclic networks, and show its tightness for a family of four-node acyclic networks when each backward link has enough capacity. For a more general family of zig-zag networks, we present conditions under which our upper bound is tight. Finally, we propose an approach for highprobability network error correction with a causal adversary. I.

Abstract—A single source network is said to be memory-free if all of the internal nodes (those except the source and the sinks) do not employ memory, but merely send linear combinations of the symbols received at their incoming edges on their outgoing edges. In this work, we introduce network-error correction for single source, acyclic, unit-delay, memory-free networks with coherent network coding for multicast. A convolutional code is designed at the source based on the network code in order to correct network-errors that correspond to any of a given set of error patterns, as long as consecutive errors are separated by a certain interval which depends on the convolutional code selected. Bounds on this interval and the field size required for constructing the convolutional code with the required free distance are also obtained. We illustrate the performance of convolutional network error correcting codes (CNECCs) designed for the unit-delay networks using simulations of CNECCs on an example network under a probabilistic error model. I.

Constant-dimension codes (CDCs) have been investigated for noncoherent error correction in random network coding. The maximum cardinality of CDCs with given minimum distance and how to construct optimal CDCs are both open problems, although CDCs obtained by lifting Gabidulin codes, referred to as KK codes, are nearly optimal. In this paper, we first construct a new class of CDCs based on KK codes, referred to as augmented KK codes, whose cardinalities are greater than previously proposed CDCs. We then propose a low-complexity decoding algorithm for our augmented KK codes using that for KK codes. Our decoding algorithm corrects more errors than a bounded subspace distance decoder by taking advantage of the structure of our augmented KK codes. In the rest of the paper we investigate the covering properties of CDCs. We first derive bounds on the minimum cardinality of a CDC with a given covering radius and then determine the asymptotic behavior of this quantity. Moreover, we show that liftings of rank metric codes have the highest possible covering radius, and hence liftings of rank metric codes are not optimal packing CDCs. Finally, we construct good covering CDCs by permuting liftings of rank metric codes. I.

Abstract—We consider packet erasure or error correction coding for a nested receiver structure, where each receiver receives a subset of the packets received by the next receiver. This type of structure arises, for instance, with temporal demands, where each receiver corresponds to a deadline by which certain information must be decoded. By making a connection with our previous work on nonmulticast network error correction, we find the capacity region for any given number of erasures or errors whose locations are a priori unknown, along with a capacityachieving intra-session coding scheme. I.

Abstract—The network communication scenario where one or more receivers request all the information transmitted by different sources is considered. We introduce the first polynomialtime (in network size) network codes that achieve any point inside the rate-region for the problem of multiple-source multicast in the presence of malicious errors, for any fixed number of sources. Our codes are fully distributed and different sources require no knowledge of the data transmitted by their peers. Our codes are “end-to-end”, that is, all nodes apart from the sources and the receivers are oblivious to the adversaries present in the network and simply implement random linear network coding. I.

Abstract—We consider the problem of correcting errors and erasures with network coding. Unlike existing works which consider performance limits for worst-case locations of given numbers of errors and erasures, we consider the performance of given (not necessarily optimal) coding and forwarding strategies for given (not necessarily worst-case) models of error and erasure locations. Our approach characterizes decoding success in terms of the rank of certain matrices corresponding to useful and erroneous information received at the sink nodes. We use this approach to analyze random coding and forwarding strategies on a family of simple networks with random error and erasure locations, and show that the relative performance of the strategies depends on the erasure and error probabilities. I.

In recent years, network coding has emerged as a new communication paradigm that can significantly improve the efficiency of network protocols by requiring intermediate nodes to mix packets before forwarding them. Recently, several real-world systems have been proposed to leverage network coding in wireless networks. Although the theoretical foundations of network coding are well understood, a real-world system needs to solve a plethora of practical aspects before network coding can meet its promised potential. These practical design choices expose network coding systems to a wide range of attacks. We identify two general frameworks (inter-flow and intra-flow) that encompass several network coding-based systems proposed in wireless networks. Our systematic analysis of the components of these frameworks reveals vulnerabilities to a wide range of attacks, which may severely degrade system performance. Then, we identify security goals and design challenges in achieving security for network coding systems. Adequate understanding of both the threats and challenges is essential to effectively design secure practical network coding systems. Our paper should be viewed as a cautionary note pointing out the frailty of current network coding-based wireless systems and a general guideline in the effort of achieving security for network coding systems. Key words: Wireless network coding, network coding attacks, network coding security 1.