Towards Optimal Broadcasting Policies for HARQ based on Fountain Codes in Underwater Networks Paolo Casari, Michele Rossi and Michele Zorzi Department of Information Engineering, University of Padova, 6/B Via G. Gradenigo, I–35131 Padova (PD), Italy E-mail: {casarip,rossi,zorzi}@dei.unipd.it Invited paper Abstract—This paper explores hybrid ARQ policies based on Fountain Codes for the transmission of multicast messages in un- derwater channels. These rateless codes are considered because of two nice properties, namely, they are computationally lightweight and do not require to know the channel erasure probabilities at the receivers prior to transmission. In this paper, these codes are used together with a Stop and Wait ARQ to enhance the performance of broadcast communications. First, we present a dynamic programming model for the characterization of optimal broadcasting policies. The derived broadcasting rules are then compared against plain ARQ schemes via Monte-Carlo simulation. Our results show that digital fountain codes are a promising technique for the transmission over underwater channels as their performance, in terms of delay, reliability and energy efficiency, clearly dominates that of plain ARQ solutions. This paper is a preliminary study on the topic and encourages us towards the design of practical HARQ protocols for the underwater medium. Index Terms—Underwater acoustic networks, broadcast, foun- tain codes, hybrid ARQ, optimal transmission policy. I. I NTRODUCTION Underwater acoustic sensor networks (UWASNs) are becom- ing increasingly popular as a research area in telecommunica- tions due to the many constraints that a transmission protocol has to face in this environment. Specifically, sufficiently long communication ranges and reliability are currently possible through the use of acoustic waves. However, the propagation of sound underwater incurs extremely long delays and only allows limited bit rates. These facts need to be taken into account in the design of any communication scheme, especially when the network operates according to the ad hoc paradigm. Research on networking protocols for UWASNs can be considered in its infancy. Previous work was done regarding MAC protocols [1]–[3] and some preliminary studies [4], [5] provide solutions for routing. There is, however, room for further work in terms of analysis and protocol design. In fact, the underwater channel has peculiar characteristics which entail the re-design or, in some cases, the invention of completely new solutions. Moreover, fundamental tradeoffs involving the use of transmission power, available bandwidth within channel access as well as the use of retransmissions and forward error This work is supported in part by NOAA’s Sea Grant College Program, Project no. NA060AR4170019. correction (FEC) at the link layer are often unexplored by the related literature. Along these lines, in this paper we look into techniques for reliable broadcasting in underwater networks. This is a fundamental service which received little attention to date, as the only available study to the best of our knowledge consists of the practical schemes in [6]. In this work we apply a new paradigm to underwater broadcasting, incorporating effective coding techniques such as the recently proposed fountain codes [7] into Automatic Repeat reQuest (ARQ) error recovery. Our main objective is to limit, as much as possible, the number of transmissions to reliably disseminate a message to a number of nodes. This is particularly critical in UWASNs, due to the high cost of transmissions [8]. In this paper, our hybrid ARQ (HARQ) solution is first modeled using dynamic programming [9]. This analysis is subsequently used to obtain optimal retransmission policies under maximum delay constraints. Optimal HARQ is finally compared with plain ARQ to measure the performance improvements which are achievable under the assumption of ideal channel access. Nevertheless, our analysis as well as the obtained results are general and can be used, in future research, for the design of practical broadcasting schemes. The paper is structured as follows. Section II presents a review of the related work in the field of network protocol design for UWASNs. In Section III we describe the underwater channel and review a model for the calculation of packet error probabilities according to channel and transmission parameters. Section IV introduces the fountain codes we use in this paper. In Section V we detail our mathematical framework, through which we obtain optimal error recovery policies for fountain- based HARQ for broadcasting in underwater channels. In Section VI simulation results are shown to demonstrate the effectiveness of these HARQ schemes, their superiority with respect to plain ARQ, as well as relevant tradeoffs. Finally, Section VII concludes the paper. II. RELATED WORK The use of acoustics for underwater communication has received increased interest in recent years. While the main use of acoustic waves is still sonar detection and ranging, as well as telemetry [10], relatively recent efforts have proven that reliable