We present a capacity-approaching coding scheme for unicast or multicast over lossy packet networks. In the scheme, all nodes perform coding, but do not wait for a full block of packets to be received before sending out coded packets. Rather, whenever they have a transmission opportunity, they form coded packets with random linear combinations of previously received packets. All coding and decoding operations in the scheme have polynomial complexity. Our analysis of the scheme shows that it is not only capacity-approaching, but that the propagation of packets carrying “innovative ” information follows that of a queueing network where every node acts as a stable M/M/1 queue. We consider networks with both lossy point-to-point and broadcast links, allowing us to model both wireline and wireless packet networks. 1

We study the problem of simultaneously disseminating multiple messages in a large network in a decentralized and distributed manner. We consider a network with n nodes and k (k = O(n)) messages spread throughout the network to start with, but not all nodes have all the messages. Our communication model is such that the nodes communicate in discrete-time steps, and in every time-step, each node communicates with a random communication partner chosen uniformly from all the nodes (known as the random phone call model). The system is bandwidth limited and in each time-step, only one message can be transmitted. The goal is to disseminate rapidly all the messages among all the nodes. We study the time required for this dissemination to occur with high probability, and also in expectation. We present a protocol based on random linear coding (RLC) that disseminates all the messages among all the nodes in O(n) time, which is order optimal, if we ignore the small overhead associated with each transmission. The overhead does not depend on the size of the messages and is less than 1 % for k = 100 and messages of size 100 KB. We also consider a store and forward mechanism without coding, which is a natural extension of gossip-based dissemination with one message in the network. We show that, such an uncoded scheme can do no better than a sequential approach (instead of doing it simultaneously) of disseminating the messages which takes Θ(n ln(n)) time, since disseminating a single message in a gossip network takes Θ(ln(n)) time. 1

Developing energy efficient strategies for the extraction, transmission, and dissemination of information is a core theme in wireless sensor network research. In this paper we present a novel system for decentralized data compression and predistribution. The system simultaneously computes random projections of the sensor data and disseminates them throughout the network using a simple gossiping algorithm. These summary statistics are stored in an efficient manner and can be extracted from a small subset of nodes anywhere in the network. From these measurements one can reconstruct an accurate approximation of the data at all nodes in the network, provided the original data is compressible in a certain sense which need not be known to the nodes ahead of time. The system provides a practical and universal approach to decentralized compression and content distribution in wireless sensor networks. Two example applications, network health monitoring and field estimation, demonstrate the utility of our method.

Abstract — Recent research has shown that network coding can be used in content distribution systems to improve the speed of downloads and the robustness of the systems. However, such systems are very vulnerable to attacks by malicious nodes, and we need to have a signature scheme that allows nodes to check the validity of a packet without decoding. In this paper, we propose such a signature scheme for network coding. Our scheme makes use of the linearity property of the packets in a coded system, and allows nodes to check the integrity of the packets received easily. We show that the proposed scheme is secure, and its overhead is negligible for large files. I.

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.

In this paper, we investigate the benefits of using a form of network coding known as Random Linear Coding (RLC) for unicast communications in a mobile Disruption Tolerant Network (DTN) under epidemic routing. Under RLC, DTN nodes store and then forward random linear combinations of packets as they encounter other DTN nodes. We first consider RLC applied to a single block of packets where (a) all packets have the same source and destination, (b) the packets have different sources but a common destination and (c) the packets each have a different source/destination pair; we also consider the case where blocks of packets arrive according to a Poisson bulk arrival process. Our performance metric of interest is the delay until the last packet in a block is delivered. We show that for the single block case, when bandwidth is constrained, applying RLC over packets destined to the same node achieves (with high probability) the minimum delay to deliver the block of data. We find through simulation that the benefit over non-network-coded packet forwarding increases further when buffer space within DTN nodes is limited. For the case of multiple blocks, our simulations show that RLC offers only slight improvement over the non-coded scenario when only bandwidth is constrained, but more significant benefits when both bandwidth and buffers are constrained. We remark that when the network is relatively loaded, RLC achieves improvements over non-coding scheme only if the spreading of the information is appropriately controlled. 1

Abstract — Network coding provides elegant solutions to many data transmission problems. The usage of coding for distributed data storage has also been explored. In this work, we study a joint storage and transmission problem, where a source transmits a file to storage nodes whenever the file is updated, and clients read the file by retrieving data from the storage nodes. The cost includes the transmission cost for file update and file read, as well as the storage cost. We show that such a problem can be transformed into a pure flow problem and is solvable in polynomial time using linear programming. Coding is often necessary for obtaining the optimal solution with the minimum cost. However, we prove that for networks of generalized tree structures, where adjacent nodes can have asymmetric links between them, file splitting — instead of coding — is sufficient for achieving optimality. In particular, if there is no constraint on the numbers of bits that can be stored in storage nodes, there exists an optimal solution that always transmits and stores the file as a whole. The proof is accompanied by an algorithm that optimally assigns file segments to storage nodes. I.

Abstract — Wireless sensor networks have been widely used for surveillance in harsh environments. In many such applications, the environmental data are continuously sensed, and data collection by a server is only performed occasionally. Hence, the sensor nodes have to temporarily store the data, and provide easy and on-hand access for the most updated data when the server approaches. Given the expensive server-to-sensor communications, the large amount of sensors and the limited storage space at each tiny sensor, continuous data collection becomes a challenging problem. In this paper, we present partial network coding (PNC) as a generic tool for the above applications. PNC generalizes the existing network coding (NC) paradigm, an elegant solution for ubiquitous data distribution and collection. Yet, PNC enables efficient storage replacement for continuous data, which is a major deficiency of the conventional NC. We prove that the performance of PNC is quite close to NC, except for a sublinear overhead on storage and communications. We then address a set of practical concerns toward PNC-based continuous data collection in sensor networks. Its feasibility and superiority are further demonstrated through simulation results. I.

Abstract — We consider the following packet coding scheme: The coding node has a fixed, finite memory in which it stores packets formed from an incoming packet stream, and it sends packets formed from random linear combinations of its memory contents. We analyze the scheme in two settings: as a selfcontained component in a network providing reliability on a single link, and as a component employed at intermediate nodes in a block-coded end-to-end connection. We believe that the scheme is a good alternative to automatic repeat request (ARQ) when feedback is too slow, too unreliable, or too difficult to implement. I.

Abstract — File distribution via network coding has received a lot of attention lately. However, direct application of network coding may have security problems. In particular, attackers can inject “faked ” packets into the file distribution process to slow down the information dispersal or even deplete the network resource. Therefore, content verification is an important and practical issue when network coding is employed. When network coding is used, it is infeasible for the source of the content to provide all the hash values or signatures required for verification, and hence the traditional “hash-and-sign ” methods are no longer applicable. Recently, a new on-the-fly verification technique is proposed by Krohn et al. for rateless erasure codes [1]. However, their scheme requires a large number of hash values to be distributed in advance, and all of them are needed to verify even for a single packet. We propose a new batch delivery and verification scheme that is similar to the classical scenario where the authentication information of a message is embedded with the message and is sufficient for the verification purpose. We investigate how our technique can be applied when random linear network coding is employed, and show that both the computational and the bandwidth overhead can be greatly reduced by using a variant of the random network coding. We further show by simulation that this variant is sufficiently effective in practice.