Distortion Exponents for Different Source- Channel Diversity Achieving Schemes over Multi-Hop Channels Karim G. Seddik 1 , Andres Kwasinski 2 , and K. J. Ray Liu 1 1 Department of Electrical and Computer Engineering, 2 Texas Instruments Inc., and Institute for Systems Research Germantown, MD 20874, USA. University of Maryland, College Park, MD 20742, USA. akwasinski@ieee.org {kseddik, kjrliu}@umd.edu Abstract— The performance limits of multimedia systems combining source (multiple description) coding and channel coding with user cooperation diversity over multi-hop channels is studied. Performance is measured through the distortion exponent, which measures the rate of decay of the end-to- end distortion at asymptotic high SNRs. Two implementations for user cooperation are considered: amplify-and-forward and decode-and-forward. Results comparing different source and channel coding schemes show that optimum channel coding diversity provides the best performance, followed by source coding diversity. The results also show that at low bandwidth expansion factor, source encoding distortion is the main limiting factor. As the bandwidth expansion factor increases, user cooperation diversity is the main limiting factor, thus, the distortion exponent could be improved by increasing the number of relays. I. I NTRODUCTION One of the most challenging problems in wireless mul- timedia communications is the need to overcome channel fading. This problem is frequently addressed through diver- sity techniques, which improves the likelihood of receiving a useful message by transmitting multiple copies of the signal in a way that each is independently affected by channel impairments. Constrains in the mobiles size and power have produced a new paradigm in diversity-exploiting techniques where mobile terminals are associated so they can help each other to ensure successful delivery of multiple copies of a message. The communication channels in this paradigm have received the generic name of relay channel [1]. We will consider a multi-hop channel where there is no direct path between the source and destination; i.e. the information path between source and destination contains one or more relaying nodes. At the signal processing level, several techniques have been proposed for the relays to forward the sources signals. Most notably, the idea of achieving spatial diversity through user cooperation was presented in [2], along with the idea of cooperation through “decode-and-forward”. In [3], the authors introduced the idea of implementing cooperation through various protocols such as the “amplify-and-forward” protocol and further studied the outage behavior of user-cooperation when using distributed space-time coding in [4]. Diversity is not exclusive to implementations at the phys- ical layer. As studied in [5], diversity can also be formed when multiple channels are provided to the application layer, where they are exploited through multiple description source encoders. In Multiple Description Coding different descriptions of the source are generated with the property that they can each be individually decoded or, if possible, be jointly decoded to obtain a reconstruction of the source with lower distortion [6]. The achievable rate-distortion performance of multiple description codes was studied in [7]. This paper focus on studying systems that exhibit diver- sity of three forms: source coding diversity (when using a dual description encoder), channel coding diversity and user-cooperation diversity (implemented through multi-hop channels, with amplify-and-forward or decode-and-forward user cooperation). The presented analysis derives the distor- tion exponent for several source-channel diversity achieving schemes. II. SYSTEM MODEL We will focus on systems that communicate a source signal over a wireless multi-hop. We will assume that communication is performed over a complex, additive white Gaussian noise (AWGN) fading channel. Denoting by I the maximum average mutual information between the channel input and output, for the channel under consideration I = log(1+|h| 2 SNR), where h is the fading value [8]. Because of the random nature of the fading, I and the ability of the channel to support transmission at some rate are themselves random. The probability of the channel not being able to support a rate R is called the outage probability and is given by P 0 = Pr[I<R]. It will be convenient for us to work with the random function e I , which has a cumulative 1-4244-0353-7/07/$25.00 ©2007 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings. 969