Energy-efficient multicasting over the erasure channel Anna Pantelidou, Kalle L¨ ahetkangas and Matti Latva-aho Centre for Wireless Communications, University of Oulu P.O. Box 4500, 90014 University of Oulu, Finland Email: {apantel, kallela, matla}@ee.oulu.fi Abstract—We consider the problem of multicasting from a single source to multiple destinations over the erasure channel. We are interested in energy efficient communication. Our performance metric is the number of bits sent per joule of energy spent until a finite amount of packets is delivered from the source to all the destinations. We compare the performance of Random Linear Network Coding (RLNC) and Automatic Repeat reQuest (ARQ) with respect to the above performance metric. Our numerical results illustrate that RLNC is more energy efficient than ARQ when the unreliability of links is high. Keywords: bits-per-joule, erasure channel, network coding, retransmissions I. I NTRODUCTION Network coding was introduced by [1] as an alternative technique to routing, where unlike the traditional technique of store-and-forward, each network node can perform operations on the packets in its queue. Since then, it has been shown to be a promising technique to improve performance under various contexts. In particular it was shown in [1] that it can achieve capacity when the symbol alphabet size grows large. The authors in [2] showed that linear codes are sufficient to achieve capacity and the authors in [3] showed that Random Linear Network Coding (RLNC) can also achieve capacity as the symbol alphabet size approaches infinity. A large symbol alphabet size implies transmitting long packets which is necessary in order to guarantee that RLNC has low overhead. This is due to the fact that the sender of a network coded packet appends also a header of overhead with the coefficients chosen for the transmission. The latter are needed for the decoding of the original packets at the receiver. As the number of symbols in packet grows large the overhead incurred by sending these coefficients becomes negligible. RLNC has received particular attention in the recent years due to its practicality and the fact that it allows distributed implementation [3]. Furthermore, RLNC has been applied recently as a means to provide reliability over unreliable wireless links. A large body of research exists along these lines where the performance of RLNC over the erasure channel is studied (see e.g., [4], [5], [6], [7], [8], [9]). In [6] and [7] the authors consider RLNC under the wireless erasure channel model. The authors assume that a The authors would like to thank the Finnish Funding Agency for Tech- nology and Innovation (Tekes), Nokia, Nokia Siemens Networks, Elektrobit (EB), and CWC for project funding. packet is either dropped with a fixed probability or is received successfully. Since in a wireless setting, longer packets are more likely to get corrupted when transmitted through the channel the assumption that the probability of erasure can be kept fixed as the alphabet size approaches infinity becomes invalid. In a subsequent work [10], the authors show that as the length of a packet increases the data rate goes to zero under an erasure wireless channel. In [8] the authors consider the energy performance of RLNC when a single source wishes to send a fixed amount of data packets to a given destination. The authors consider a Time Division Duplexing (TDD) channel model where the source has to stop transmitting packets in order to listen to the acknowledgement from the receiver informing it how many more coded packets it needs before decoding the original packets. The authors show that there exists an optimal number of coded data packets that have to be transmitted one after the other before stopping to wait for the receiver’s acknowledgement. Furthermore, in [9] the authors consider a model where an access point wants to multicast data to a set of receivers. The authors compare the reliability performance of RLNC and Automatic Repeat reQuest (ARQ) with respect to the expected number of transmissions required to deliver a packet under the aforementioned two schemes. In this work we study the problem of multicasting a finite amount of data packets from a source to a set of destinations. We are interested in energy efficient network operation where the metric of energy efficiency is the number of bits that the source can communicate to all the destinations per joule of energy spent. We compare the performance of RLNC and ARQ with respect to the above metric. Our work is different from [8] in that we consider the problem of multicasting to multiple destinations. In addition, here we look at a different metric on the network energy efficiency. Furthermore, our work is different from [9] in that we are interested in energy efficiency rather than reliability performance. Also, unlike [9], we consider a model that takes the parameters of the physical layer into account in computing the probability of packet erasure. In particular, our model captures the fact that the probability of erasure depends on the Signal to Noise Ratio (SNR) per bit at the receiver, the particular modulation technique employed for the transmission, and on the number of bits packed in a symbol. The rest of the paper is organized as follows. In Section II 978-1-61284-231-8/11/$26.00 ©2011 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2011 proceedings