Rui A. Costa

Effective Delay Control in Online Network Coding

Motivated by streaming applications with stringent delay constraints, we consider the design of online network coding algorithms with timely delivery guarantees. Assuming that the sender is providing the same data to multiple receivers over independent packet erasure channels, we focus on the case of perfect feedback and heterogeneous erasure probabilities. Based on a general analytical framework for evaluating the decoding delay, we show that existing ARQ schemes fail to ensure that receivers with weak channels are able to recover from packet losses within reasonable time. To overcome this problem, we re-define the encoding rules in order to break the chains of linear combinations that cannot be decoded after one of the packets is lost. Our results show that sending uncoded packets at key times ensures that all the receivers are able to meet specific delay requirements with very high probability.

Informed network coding for minimum decoding delay

Network coding is a highly efficient data dissemination mechanism for wireless networks. Since network coded information can only be recovered after delivering a sufficient number of coded packets, the resulting decoding delay can become problematic for delay-sensitive applications such as real-time media streaming. Motivated by this observation, we consider several algorithms that minimize the decoding delay and analyze their performance by means of simulation. The algorithms differ both in the required information about the state of the neighborspsila buffers and in the way this knowledge is used to decide which packets to combine through coding operations. Our results show that a greedy algorithm, whose encodings maximize the number of nodes at which a coded packet is immediately decodable significantly outperforms existing network coding protocols.

On the Delay Distribution of Random Linear Network Coding

A fundamental understanding of the delay behavior of network coding is key towards its successful application in real-time applications with strict message deadlines. Previous contributions focused mostly on the average decoding delay, which although useful in various scenarios of interest is not sufficient for providing worst-case delay guarantees. To overcome this challenge, we investigate the entire delay distribution of random linear network coding for any field size and arbitrary number of encoded symbols (or generation size). By introducing a Markov chain model we are able to obtain a complete solution for the erasure broadcast channel with two receivers. A comparison with Automatic Repeat reQuest (ARQ) with perfect feedback, round robin scheduling and a class of fountain codes reveals that network coding on GF(24) offers the best delay performance for two receivers. We also conclude that GF(2) induces a heavy tail in the delay distribution, which implies that network coding based on XOR operations although simple to implement bears a relevant cost in terms of worst-case delay. For the case of three receivers, which is mathematically challenging, we propose a brute-force methodology that gives the delay distribution of network coding for small generations and field size up to GF(24).

Real-Time Network Coding for Live Streaming in Hyper-Dense WiFi Spaces

Consumer demand for high-quality video over wireless networks is increasing at fast pace. The resulting technical challenges are particularly stringent in crowded spaces, where the density of users far exceeds the ability to deploy cellular base stations or WiFi infrastructure in a cost effective way. To address this problem, we present a reliable and scalable live streaming solution based on wireless multicast with real-time network coding. At the core of our approach is a timely delivery scheme that uses a minimum amount of feedback from the receivers to generate coded repair packets that are simultaneously useful to a large number of users. Our protocol, which we implemented and tested in a real-world wireless testbed, differs from traditional wireless unicast and multicast schemes in that (a) the feedback messages of the users are treated jointly and (b) the repair mechanism considers both the playout deadlines of individual packets and the list of packets already received by the clients. In comparison with a standard video approach that sends an MPEG-2 encoded stream over 802.11 unicast links, our solution offers real-time guarantees for all users commensurate with the link quality and an 11x improvement in terms of bandwidth usage. A commercial version of the proposed solution shows a strong increase in the number of clients that can access video streams simultaneously over a single WiFi hotspot.

Harbornet: a real-world testbed for vehicular networks

We present a real-world testbed for research and development in vehicular networking that has been deployed successfully in the seaport of Leixoes in Portugal. The testbed allows cloudbased code deployment, remote network control and distributed data collection from moving container trucks, cranes, tow boats, patrol vessels, and roadside units, thereby enabling a wide range of experiments and performance analyses. After describing the testbed architecture and its various modes of operation, we give concrete examples of its use and offer insights on how to build effective testbeds for wireless networking with moving vehicles.

Network Information Flow in Navigable Small-World Networks

Small-world graphs, exhibiting high clustering co-efficients and small average path length, have been shown to capture fundamental properties of a large number of natural and man-made networks. In the context of communication networks, navigable small-world topologies, i.e. those which admit efficient distributed routing algorithms, are deemed particularly effective, for example in resource discovery tasks and peer-to-peer applications. Intrigued by the fundamental limits of communication in networks that exploit this type of topology, we study two classes of navigable small-world networks from the point of view of network information flow and provide inner and outer bounds for their max-flow min-cut capacity. Our contribution is in contrast with the standard approach to small world networks which privileges parameters pertaining to connectivity.

One-shot capacity of discrete channels

Shannon defined channel capacity as the highest rate at which there exists a sequence of codes of block length n such that the error probability goes to zero as n goes to infinity. In this definition, it is implicit that the block length, which can be viewed as the number of available channel uses, is unlimited. This is not the case when the transmission power must be concentrated on a single transmission, most notably in military scenarios with adversarial conditions or delay-tolerant networks with random short encounters. A natural question arises: how much information can we transmit in a single use of the channel? We give a precise characterization of the one-shot capacity of discrete channels, defined as the maximum number of bits that can be transmitted in a single use of a channel with an error probability that does not exceed a prescribed value. This capacity definition is shown to be useful and significantly different from the zero-error problem statement.

Dual Radio Networks: Capacity and Connectivity

Motivated by the proliferation of dual radio devices, we consider a wireless network model in which all devices have short-range transmission capability, but a subset of the nodes has a secondary long-range wireless interface. For the resulting class of random graph models, we present analytical bounds for both the connectivity and the max-flow min-cut capacity. Perhaps the most striking conclusion to be drawn from our results is that the capacity of this class grows quadratically with the fraction of dual radio devices, thus indicating that a small percentage of such devices is sufficient to improve significantly the capacity of the network.

Non-Asymptotic Analysis of Network Coding Delay

We present an expression for the delay distribution of Random Linear Network Coding over an erasure channel with a given loss probability. In contrast with previous contributions, our analysis is non- asymptotic in the sense that it is valid for any field size and any number of symbols. The results confirm that GF(16) already offers near-optimal decoding delay, whereas smaller field sizes (e.g. requiring only XOR operations) induce heavy tails in the delay distribution. A comparison with Automatic Repeat reQuest (ARQ) techniques (with perfect feedback) is also included.