Outer bounds on the error correction capacity region for non-multicast networks

In this paper we study the capacity regions of non-multicast networks that are susceptible to adversarial errors. We derive outer bounds on the error correction capacity region and give a family of single- and two-source two-sink 3-layer networks for which these bounds are tight

On the Delay of Network Coding over Line Networks

We analyze a simple network where a source and a receiver are connected by a line of erasure channels of different reliabilities. Recent prior work has shown that random linear network coding can achieve the min-cut capacity and therefore the asymptotic rate is determined by the worst link of the line network. In this paper we investigate the delay for transmitting a batch of packets, which is a function of all the erasure probabilities and the number of packets in the batch. We show a monotonicity result on the delay function and derive simple expressions which characterize the expected delay behavior of line networks. Further, we use a martingale bounded differences argument to show that the actual delay is tightly concentrated around its expectation

On the Delay Advantage of Coding in Packet Erasure Networks

We consider the delay of network coding compared to routing with retransmissions in packet erasure networks with probabilistic erasures. We investigate the sublinear term in the block delay required for unicasting n packets and show that there is an unbounded gap between network coding and routing. In particular, we show that delay benefit of network coding scales at least as √n. Our analysis of the delay function for the routing strategy involves a major technical challenge of computing the expectation of the maximum of two negative binomial random variables. Previous characterizations of this expectation are approximate; we derive an exact characterization and analyze its scaling behavior, which may be of independent interest. We also use a martingale bounded differences argument to show that the actual coding delay is concentrated around its expectation

On Delay and Security in Network Coding

In this thesis, delay and security issues in network coding are considered. First, we study the delay incurred in the transmission of a fixed number of packets through acyclic networks comprised of erasure links. The two transmission schemes studied are routing with hop-by-hop retransmissions, where every node in the network simply stores and forwards its received packets, and linear coding, where nodes mix their packets by forwarding linear combinations of all their previously received packets. We show that even though the achievable rates of coding and routing are the same, network coding can have an increasingly better performance than routing as the number of packets increases. Secondly, we investigate the security benefits of network coding. We investigate the achievable secrecy rate region in a general network of noisy wiretap channels with general communication demands. The eavesdropper has access to an unknown set of links, and on the wiretapped links observes a degraded version of the intended receiver's observation. While characterizing the capacity in general is an open problem, in the noise-free case there exist inner and outer bounds. In the noisy case, we show how one can change any of the wiretap channels to a noiseless degraded broadcast channel, so that the derived network's rate region bounds, and under certain conditions is equivalent, to that of the initial network. Specifically, we showed that in case the eavesdropper can choose only a single link to wiretap at each time, then one can change all the links in the network with corresponding noiseless ones, creating an equivalent noiseless secrecy problem. In the case where the eavesdropper can wiretap multiple links simultaneously, we derive upper and lower bounding noiseless network problems. Finally, we consider design practical code design for the detection of adversarial errors in a distributed storage system. We build on work of functions that can fool linear polynomials to create and communicate hash functions of the data in order to detect with high probability the maliciously attacked nodes in the system.</p

Multi-source operator channels: Efficient capacity-achieving codes

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

On the Delay Advantage of Coding in Packet Erasure Networks

We consider the delay of network coding compared to routing for a family of simple networks with parallel links. We investigate the sub-linear term in the block delay required for unicasting n packets and show that there is an unbounded gap between network coding and routing. In particular, we show that delay benefit of network coding is scaling at least as fast as √ n. The main technical contribution involves showing that the delay function for the routing retransmission strategy is unbounded. This problem turns out to be equivalent with computing the expected maximum of two negative binomial random variables. This problem has also been addressed previously and we derive the first exact characterization which might be of independent interest