Binary Systematic Network Coding for Progressive Packet Decoding

We consider binary systematic network codes and investigate their capability of decoding a source message either in full or in part. We carry out a probability analysis, derive closed-form expressions for the decoding probability and show that systematic network coding outperforms conventional network coding. We also develop an algorithm based on Gaussian elimination that allows progressive decoding of source packets. Simulation results show that the proposed decoding algorithm can achieve the theoretical optimal performance. Furthermore, we demonstrate that systematic network codes equipped with the proposed algorithm are good candidates for progressive packet recovery owing to their overall decoding delay characteristics.Comment: Proc. of IEEE ICC 2015 - Communication Theory Symposium, to appea

Systematic Network Coding with the Aid of a Full-Duplex Relay

A characterization of systematic network coding over multi-hop wireless networks is key towards understanding the trade-off between complexity and delay performance of networks that preserve the systematic structure. This paper studies the case of a relay channel, where the source's objective is to deliver a given number of data packets to a receiver with the aid of a relay. The source broadcasts to both the receiver and the relay using one frequency, while the relay uses another frequency for transmissions to the receiver, allowing for a full-duplex operation of the relay. We analyze the decoding complexity and delay performance of two types of relays: one that preserves the systematic structure of the code from the source; another that does not. A systematic relay forwards uncoded packets upon reception, but transmits coded packets to the receiver after receiving the first coded packet from the source. On the other hand, a non-systematic relay always transmits linear combinations of previously received packets. We compare the performance of these two alternatives by analytically characterizing the expected transmission completion time as well as the number of uncoded packets forwarded by the relay. Our numerical results show that, for a poor channel between the source and the receiver, preserving the systematic structure at the relay (i) allows a significant increase in the number of uncoded packets received by the receiver, thus reducing the decoding complexity, and (ii) preserves close to optimal delay performance.Comment: 6 pages, 5 figures, submitted to IEEE Globeco

Network Coding Over SATCOM: Lessons Learned

Satellite networks provide unique challenges that can restrict users' quality of service. For example, high packet erasure rates and large latencies can cause significant disruptions to applications such as video streaming or voice-over-IP. Network coding is one promising technique that has been shown to help improve performance, especially in these environments. However, implementing any form of network code can be challenging. This paper will use an example of a generation-based network code and a sliding-window network code to help highlight the benefits and drawbacks of using one over the other. In-order packet delivery delay, as well as network efficiency, will be used as metrics to help differentiate between the two approaches. Furthermore, lessoned learned during the course of our research will be provided in an attempt to help the reader understand when and where network coding provides its benefits.Comment: Accepted to WiSATS 201

On Code Parameters and Coding Vector Representation for Practical RLNC

Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. The drawbacks associated with it are the complexity of the decoding and the overhead resulting from the encoding vector. Increasing the field size and generation length presents a fundamental trade-off between packet-based throughput and operational overhead. On the one hand, decreasing the probability of redundant packets' being transmitted is beneficial for throughput and, consequently, reduces transmission energy. On the other hand, the decoding complexity and amount of header overhead increase with field size and generation length, leading to higher energy consumption. The main findings of this work are bounds for the transmission overhead due to linearly dependent packets. The optimal trade-off is system and topology dependent, as it depends on the cost in energy of performing coding operations versus transmitting data. We show that moderate field sizes are the correct choice when trade-offs are considered. The results show that sparse binary codes perform the best, unless the generation size is very low.Cooperation and Network Coding Project (CONE) (Grant 09-066549/FTP

Whether and Where to Code in the Wireless Relay Channel

The throughput benefits of random linear network codes have been studied extensively for wirelined and wireless erasure networks. It is often assumed that all nodes within a network perform coding operations. In energy-constrained systems, however, coding subgraphs should be chosen to control the number of coding nodes while maintaining throughput. In this paper, we explore the strategic use of network coding in the wireless packet erasure relay channel according to both throughput and energy metrics. In the relay channel, a single source communicates to a single sink through the aid of a half-duplex relay. The fluid flow model is used to describe the case where both the source and the relay are coding, and Markov chain models are proposed to describe packet evolution if only the source or only the relay is coding. In addition to transmission energy, we take into account coding and reception energies. We show that coding at the relay alone while operating in a rateless fashion is neither throughput nor energy efficient. Given a set of system parameters, our analysis determines the optimal amount of time the relay should participate in the transmission, and where coding should be performed.Comment: 11 pages, 12 figures, to be published in the IEEE JSAC Special Issue on Theories and Methods for Advanced Wireless Relay

Band Codes for Energy-Efficient Network Coding with Application to P2P Mobile Streaming

A key problem in random network coding (NC) lies in the complexity and energy consumption associated with the packet decoding processes, which hinder its application in mobile environments. Controlling and hence limiting such factors has always been an important but elusive research goal, since the packet degree distribution, which is the main factor driving the complexity, is altered in a non-deterministic way by the random recombinations at the network nodes. In this paper we tackle this problem proposing Band Codes (BC), a novel class of network codes specifically designed to preserve the packet degree distribution during packet encoding, ecombination and decoding. BC are random codes over GF(2) that exhibit low decoding complexity, feature limited and controlled degree distribution by construction, and hence allow to effectively apply NC even in energy-constrained scenarios. In particular, in this paper we motivate and describe our new design and provide a thorough analysis of its performance. We provide numerical simulations of the performance of BC in order to validate the analysis and assess the overhead of BC with respect to a onventional NC scheme. Moreover, peer-to-peer media streaming experiments with a random-push protocol show that BC reduce the decoding complexity by a factor of two, to a point where NC-based mobile streaming to mobile devices becomes practically feasible.Comment: To be published in IEEE Transacions on Multimedi