IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 58, NO. 2, FEBRUARY2009 655 A Convolutional-Based Distributed Coded Cooperation Scheme for Relay Channels Mohamed Elfituri, Member, IEEE, Walaa Hamouda, Senior Member, IEEE, and Ali Ghrayeb, Senior Member, IEEE Abstract—In this paper, we consider a coded cooperation di- versity scheme that is suitable for L-relay channels that operate in the decode–forward mode. The proposed scheme is based on convolutional coding, where each codeword of the source node is partitioned into two frames that are transmitted in two phases. In the first phase, the first frame is broadcast from the source to the relays and destination. In the second phase, the second frame is transmitted on orthogonal subchannels from the source and relay nodes to the destination. Each relay is assumed to be equipped with a cyclic redundancy check (CRC) code for error detection. Only these relays (whose CRCs check) transmit in the second phase. Otherwise, they keep silent. At the destination, the received replicas (of the second frame) are combined using maximal ratio combining. The entire codeword, which comprises the two frames, is decoded via the Viterbi algorithm. We analyze the proposed scheme in terms of its probability of bit error and outage probability. Explicit upper bounds are obtained, assuming M -ary phase-shift keying transmission. Our analytical results show that the full diversity order is achieved, provided that the source-relay link is more reliable than the other links. Otherwise, the diversity degrades. However, in both cases, it is shown that it is possible to achieve substantial performance improvements over noncooperative coded systems. Several numerical and simulation results are presented to demonstrate the efficacy of the proposed scheme. Index Terms—Channel coding, coded cooperation, error prob- ability, fading channels, outage event probability, pairwise error probability, relay channels. I. I NTRODUCTION D IVERSITY techniques are known to provide an efficient way of combating fading in wireless communication en- vironments. Time, frequency, and spatial diversity are the three main forms of these diversity techniques [1]–[4]. Time diversity is used in the form of channel coding, in conjunction with time interleaving, where replicas of the transmitted signal are provided to the receiver in the form of redundancy in the tempo- ral domain. Waves that are transmitted at different frequencies induce different multipath structure in the propagation media, where frequency diversity can be exploited. In most wireless systems, antenna diversity is a practical effective widely ap- Manuscript received June 20, 2007; revised October 25, 2007, January 31, 2008, April 16, 2008, and May 16, 2008. First published June 6, 2008; current version published February 17, 2009. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Grant N00861 and Grant N00858. This paper was presented at the International Conference on Communications (ICC08). The review of this paper was coordinated by Prof. S. Cui. The authors are with the Department of Electrical and Computer Engineering, Concordia University, Montreal, QC H3G 1M8, Canada (e-mail: m_elfitu@ece.concordia.ca; hamouda@ece.concordia.ca; aghrayeb@ece. concordia.ca). Digital Object Identifier 10.1109/TVT.2008.927033 plied diversity technique [5]. It has been shown that a system with multiple-transmitter–multiple-receiver antennas [multiple- input–multiple-output (MIMO)] improves the received signal quality through diversity [6]–[8]. In these systems, each pair of transmitter–receiver antennas provides an independent path from the transmitter to the receiver. By proper encoding, mul- tiple independent faded replicas of a signal are obtained at the receiver side, thus creating spatial diversity. Furthermore, it is possible to achieve higher spectral efficiency in MIMO systems compared with single-input–single-output systems through spa- tial multiplexing. However, these improvements come at the cost of requiring multiple radio frequency front ends at both the transmitter and the receiver. Furthermore, the size of mobile devices may limit the number of antennas that can be deployed. As an alternative to using collocated antennas at the transmit- ter and/or receiver, one can achieve the same spatial diversity gain through cooperative diversity [9]–[13]. In cooperative communications, multiple nodes in a wireless network work together to form a virtual antenna array. Using cooperation, it is possible to exploit the spatial diversity of the traditional MIMO techniques, without each node necessarily having mul- tiple antennas. The destination receives multiple versions of the message from the source and one or more relays and combines these to obtain a more reliable estimate of the transmitted signal and higher data rates. These cooperative techniques utilize the broadcast nature of wireless signals by observing that a source signal that was intended for a particular destination can be “overheard” at neighboring nodes. These nodes, called relays, partners, or helpers, process the signals that they overhear and transmit toward the destination. In cooperative diversity, nodes can cooperate with each other to provide spatial diversity gain at the destination. In this case, at any given time, any node can be a source, a relay, or a destination. The function of the relay node is to assist in the transmission of the source information to the destination node. To ensure diversity gains, the relay is chosen in such a way that its link to the destination is independent of the link to the source. Within the framework of cooperative diversity, there are two main cooperative diversity techniques for transmis- sion between a pair of nodes through a multiple relay nodes: 1) amplify–forward (AF) [14] and 2) decode–forward (DF) modes [9], [15]. In the AF mode, the relay simply amplifies and retransmits the signal received from the source (the signal that is received at the relay terminal is corrupted by fading and additive noise). No demodulation or decoding of the received signal is required in this case. On the other hand, in the DF mode, the received signal from the source terminal is demodulated and decoded before retransmission. Most of the previous 0018-9545/$25.00 © 2009 IEEE