The Maximum Achievable Throughput of a Decode-and-Forward Based Hybrid-ARQ Protocol Ilmu Byun and Kwang Soon Kim t Department of Electrical and Electronic Engineering, Yonsei University 134, Shinchong Dong, Seodaemun Gu, Seoul 120-749, Korea E-mail: [dlfanv ks.kirnj Oyonsei.ac.kr t Corresponding Author ABSTRACT Cooperative hybrid-ARQ (HARQ) protocols have been widely studied because they are more efficient than coop- erative protocols without HARQ. In [7J, the throughput of a cooperative HARQ protocol based on the decode-and- forward protocol (DF-HARQ) is obtained. In this paper, the maximum achievable throughput of the DF-HARQ pro- tocol is obtained using the asymptotic outage probability when the maximum number of transmission (M) goes to infinity. The range of the optimum worst-case coding rate (R) of the maximum achievable throughput is also obtained. Furthermore, we can expect that the method- ology for obtaining the maximum achievable throughput in this paper also applicable to other cooperative HARQ protocols INTRODUCTION To achieve more reliable communication and improve the efficiency of cooperative communications, cooperative ARQ or hybrid-ARQ (HARQ) protocols have been widely studied [1]-[3]. In [1], it was shown that the incremental relaying protocol based on the limited feedback from the destination, which can be viewed as an extension of a ARQ into a cooperative context, outperforms the fixed relaying protocol. In [2], the dynamic decode-and-forward (DDF) based ARQ protocol was proposed. It can achieve the optimum diversity-multiplexing tradeoff in a single relay channel when the maximum allowable number of transmission is greater than 1. On the other side, in [3], it was shown that an ARQ protocol can improve performance by combining it with a cooperative protocol. There have been many further researches to develop and analyze cooperative ARQ or HARQ protocols due to their performance improvement [4]-[6]. In [4], three cooperative ARQ protocols based on the incremental re- laying and the selection relaying protocols were proposed and their approximated packet error rate was obtained. In [5] and [6], cooperative HARQ protocols for multiple relays were analyzed for the Chase combining and the incremental redundancy (IR) schemes. The upper bound 978-1-4244-5239-2/09/$26.00 ©2009 IEEE of the throughput of a cooperative incremental redundancy (IR) HARQ protocol was developed for a scenario where relays are close to a source [5]. However, in practical wireless systems, the relay can be selected from various locations. Thus, in [7], the performance of a cooperative IR-HARQ protocol is analyzed and the optimum initial transmission rate is also searched stepwisely according to the overall relay location. The analyzed cooperative IR-HARQ protocol in [7] is a decode-and-forward based HARQ (DF-HARQ) protocol in which an extended version of the protocol 1 in [4]. The advantages of the DF-HARQ are that it can achieve full diversity order and it is much easier to implement for practical systems. In this paper, the maximum achievable throughput (i.e. the throughput when M goes to infinity) of the DF-HARQ protocol and the range of the optimum worst-case coding rate (R = r / M) is obtained for block fading channels. They are simply expressed as the terms of the ergodic capacity of each link. Furthermore, we can expect that the maximum achievable throughput of various protocols can be compared using the methodology developed in this paper. SYSTEM MODEL AND PROTOCOL DESCRIPTION A single relay cooperative ARQ model with three half- duplex terminals (a source, a destination, and a relay) is assumed as in [4]. The source transmits data to the destination with the aid of the relay. The destination sends one-bit feedback (ACKINACK) to the source and the relay for retransmission. Also, the relay sends one-bit feedback to the source. We assume that ACKINACK messages are decoded without error. A. Protocol Description One round of the DF-HARQ protocol is comprised of two steps. In Step 1, the source broadcasts a packet to the destination and the relay until one of them success- fully decodes or the number of transmission reaches to the maximum number of transmission. If the destination