Dynamic Decode-and-Forward Relaying using Raptor Codes

A Ravanshid, L Lampe, J B Huber
2011 IEEE Transactions on Wireless Communications  
Dynamic decode-and-forward (DDF) is a version of decode-and-forward relaying in which the duration of the listening phase at relays is not fixed. In this paper, we investigate half-duplex DDF relaying based on rateless codes. The use of rateless codes allows relays to autonomously switch from listening to the source node to transmitting to the destination node. We first revisit different signal combining strategies applied at the destination node, namely energy and information combining known
more » ... om literature, and propose a new combining method which we refer to as mixed combining. The different combining methods give rise to different achievable rates, i.e., constrained channel capacities, for which we provide analytical expressions. The capacity analysis reveals the conditions under which mixed combining is superior and how it can be optimized. We then consider Raptor codes as a specific implementation of rateless codes and develop a density-evolution approximation to predict the data-rate performance of these codes in DDF relaying. Furthermore, we devise an optimization of the output symbol degree distribution of Raptor codes that is mainly used to benchmark the performance of Raptor codes with a fixed degree distribution. Numerical results for exemplary three-node and four-node relay networks show that the proposed mixed combining provides significant gains in achievable data rate and that Raptor codes with a fixed degree distribution are able to realize these gains and to approach closely the constrained-capacity limits. DRAFT 1 I. INTRODUCTION In the wake of advances in multiple-antenna transmission and with the ongoing evolution towards network communication theory, the study of cooperative communications in wireless networks has experienced a recent revival, e.g. [1]-[5]. Cooperative communications can achieve spatial diversity and multiplexing without requiring multiple-antennas to be collocated in a single device. The three-terminal relay channel, as the fundamental unit of cooperative communications, was introduced in the pioneering work [6] and thoroughly analyzed in [7]. Although early information theoretic studies on cooperative communications focussed on full-duplex relaying, in recent years a lot of research has been directed towards practical protocols based on half-duplex relaying, where the relay is not able to receive and transmit simultaneously, e.g. [1]-[4], [8]. Among the various strategies that enable relays to assist the source-to-destination communication link, the decode-andforward (DF) strategy has attracted great attention. In DF, the transmission interval is divided into a listening phase, during which a relay only receives, and a collaboration phase, during which the relay transmits the successfully decoded source message. The duration of the listening phase can be predetermined [3], [4] or it can be adapted to the actual quality of the source-to-relay channel [8]- [11] . In case of the latter, and in the absence of channel state information (CSI) at the sender, the relay would decide on its own when to switch from listening to collaborating, which is also referred to as dynamic decode-and-forward (DDF) [10] . Recently, starting with [12], the application of rateless codes, in particular Luby transform (LT) and Raptor codes [13], [14] , has been advocated to accomplish DDF with a flexible duration of the listening phase. While [12] considered the three-node relay channel with non-orthogonal source-to-destination and relay-todestination channels, relaying with multiple relay nodes and orthogonal subchannels were studied in [15] . The assumption of orthogonal channels enables the use of two different signal combining schemes at receiving nodes (destination and relays) during the collaboration phase, which are referred to as energy combining (EC) and information combining (IC) in [15] . In the context of collaboration using fixed-rate codes, the concepts of EC and IC are also known as DF with repetition coding and coded cooperation, respectively [4]. In this paper, we study half-duplex DDF transmission using rateless codes. As in [15], we consider orthogonal source-to-destination and relay-to-destination channels, and as in [12] , [15] we assume that the destination node knows when a relay starts to transmit, which can be accomplished by, e.g., assigning relay-specific spreading sequences. We first consider signal combining when multiple signals are received during the collaboration phase of DDF. We formulate EC and IC in a common framework and introduce a new combining scheme, which is a hybrid of EC and IC and which we refer to as mixed combining (MC). We derive the pertinent capacity limits February 1, 2011 DRAFT
doi:10.1109/twc.2011.030411.100834 fatcat:rnhofxkcobdl5euxetfhczvehq