An Optimal Adaptive Network Coding Scheme for Minimizing Decoding Delay in Broadcast Erasure Channels

Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2010, Article ID 618016, 14 pages doi:10.1155/2010/618016 Research Article An Optimal Adaptive Network Coding Scheme for Minimizing Decoding Delay in Broadcast Erasure Channels Parastoo Sadeghi,1 Ramtin Shams,1 and Danail Traskov2 1 Research School of Information Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia 2 Institute for Communications Engineering, Technische Universität München, D-80290 München, Germany Correspondence should be addressed to Parastoo Sadeghi, Received 31 August 2009; Accepted 3 March 2010 Academic Editor: Heung-No Lee Copyright © 2010 Parastoo Sadeghi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We are concerned with designing feedback-based adaptive network coding schemes with the aim of minimizing decoding delay in each transmission in packet-based erasure networks. We study systems where each packet brings new information to the destination regardless of its order and require the packets to be instantaneously decodable. We first formulate the decoding delay minimization problem as an integer linear program and then propose efficient algorithms for finding its optimal solution(s). We show that our problem formulation is applicable to memoryless erasures as well as Gilbert-Elliott erasures with memory. We then propose a number of heuristic algorithms with worst case linear execution complexity that can be used when an optimal solution cannot be found in a reasonable time. We verify the delay and speed performance of our techniques through numerical analysis. This analysis reveals that by taking channel memory into account in network coding decisions, one can considerably reduce decoding delays. 1. Introduction In this paper, we are concerned with designing feedbackbased adaptive network coding schemes that can deliver high throughputs and low decoding delays in packet erasure networks. We first present some background on existing work and emphasize that the notion of delay and the choice of a suitable network coding strategy are highly entangled with the underlying application. 1.1. Motivation and Background. Consider a broadcast packet-based transmission from one source to many destinations where erasures can occur in the links between the source and destinations. Two main throughput optimal schemes to deal with such erasures are fountain codes [1] and random linear network codes (RLNC) [2]. In the latter scheme, for example, the source transmits random linear mixtures of all the packets to be delivered. It is well-known that if the random coefficients are chosen from a finite field with a sufficiently large size, each coded packet will almost surely become linearly independent of all previously received coded packets and hence, innovative for every destination [2]. The scheme is therefore almost surely throughput optimal. Another benefit of fountain codes and RLNC is that they do not require feedback about erasures in individual links in order to operate. However in these schemes, throughput optimality comes at the cost of large decoding delays, as the receiver needs, in general, to collect all coded packets in a block before being able to decode. Despite this drawback, there are applications which are insensitive to such delays. Consider, for example, a simple software update (file download). The update only starts to work when the whole file is downloaded. In this case, the main desired properties are throughput optimality and the mean completion time and there is often little or no incentive to aim for partial “premature” decoding. The completion time performance of RLNC for rateless file download applications has been considered in [3]. In [3], the mean completion time of RLNC is shown to be much shorter than scheduling. Reference [4] considers time division duplex systems with large round-trip link latencies and proposes solutions for the number of coded packet 2 EURASIP Journal on Wireless Communications and Networking transmissions before waiting for acknowledgement on the received number of degrees of freedom. There are applications where partial decoding can crucially influence the end user’s experience. Consider, for example, broadcasting a continuous stream of video or audio in live or playback modes. Even though fountain codes and RLNC are throughput optimal, having to wait for the entire coded block to arrive can result in unacceptable delays in the application layer. But, we also note that partial decoding of packets out of their natural temporal order does not necessarily translate into low delivery delays desired by the application layer. The authors in [5, 6] have proposed feedback-based throughput-optimal schemes to deal with the transmitter queue size, as well as decoding and delivery delays at the destinations. When the traffic load approaches system capacity, their methods are shown to behave “gracefully” and meet the delay performance benchmark of singlereceiver automatic repeat request (ARQ) schemes. There is yet another set of applications for which partial decoding is beneficial and can result in lower delays irrespective of the order in which packets are being decoded. Consider, for example, a wireless sensor network in which there is a fusion/command center together with numerous sensors/agents scattered in a region. Each sensor/agent has to execute or process one or more complex commands. Each command and its associated data is dispatched from the center in a packet. For coordination purposes, each agent needs to know its own and other agents’ commands. Therefore, commands are broadcast to everyone in the network. In this application, in-order processing/execution of commands may not be a real issue. However, fast command execution may be crucial and therefore, it is imperative that innovative packets arrive and get decoded at the destinations as quickly as possible regardless of their order. As another example, consider emergency operations in a large geographical region where emergency-related updates of the map of the area need to be dispatched to all emergency crew members. In such situations too, updates of different parts of the map can be decoded in any order and still be useful for handling the emergency. Finally, some applications may be designed in such a way that they are insensitive to in-order delivery. This can be particularly useful where the transport medium is unreliable. In such a case, it may be natural to use multiple-description source coding techniques [7], in which every decoded packet brings new information to the destination, irrespective of its order. In light of the emergency applications described above, one can perform multiple-description coding for map updates, so that upd (...truncated)