On Strategies for Source Information Transmission over MIMO Systems Marco Zoffoli ∗ Dept. of Electrical and Computer Eng. University of California, Santa Barbara Jerry D. Gibson † Dept. of Electrical and Computer Eng. University of California, Santa Barbara Email: gibson@ece.ucsb.edu Marco Chiani DEIS University of Bologna 47023 Cesena, Italy Abstract—We consider strategies for the lossy transmission of a zero mean Gaussian source over a 2×2 MIMO channel with Rayleigh fading. The source is represented either using a single description or a multiple description code, depending on each strategy characteristic. Performance is evaluated using normalized expected distortion at the receiver, as a function of outage probability. The first strategy employs repetition coding over the two transmit antennas for the transmission of a single description representation of the source. The second strategy uses a time-shared approach to the two transmit antennas, allowing for the transmission of a multiple description representation of the source. The third and fourth strategies are based on, respectively, the Alamouti scheme and spatial multiplexing, and both of these strategies are used for the transmission of a single description representation of the source. The results show that the spatial multiplexing strategy is able to achieve the lowest distortion, and also that it is possible, with the Alamouti strategy, to obtain similar performance at a lower complexity. We finally consider the outage rates of the different strategies and observe that if a system is designed to maximize the outage rate, the corresponding distortion observed at the receiver will not be minimized. I. I NTRODUCTION A Multiple-Input Multiple-Output (MIMO) system is a system that employs multiple antennas both at the transmitter and receiver. The first theoretical analyses of MIMO systems were developed by Winters [1], Foschini [2] and Telatar [3], as well as others, and since then there have been many research efforts on this subject. What mainly makes MIMO systems interesting is their potential ability to achieve an increase in system capacity or in link reliability without requiring additional transmission power or bandwidth [4]. In this work, we focus on the utilization of MIMO systems for the lossy transmission of source information. In particu- lar, we want to compare several different strategies for the transmission of a zero mean Gaussian source over a 2×2 MIMO channel with Rayleigh fading. These strategies are based on techniques such as Repetition coding (REP) [5], Time Sharing (TS), the Alamouti scheme (ALM) [5], [6] and Spatial ∗ Currently visiting from University of Bologna. † Corresponding author. This research has been supported by the California Micro Program, Applied Signal Technology, Cisco, Dolby Labs, Inc., by Qualcomm, Inc, by NSF Grant Nos. CCF-0429884, CNS-0435527, CCF-0728646, and by the European Community under Seventh Framework Programme grant agreement ICT OPTIMIX n ◦ INFSO-ICT-214625. Multiplexing (SM) [5]. Depending on its characteristics, each strategy will be used either for the transmission of a Single Description (SD) or the transmission of a Multiple Description (MD) representation of this source. In SD coding, a single stream of information describing the source is transmitted over a single channel. In MD coding [7], the source is represented using two different descriptions that are transmitted over two independent channels. If both descriptions are correctly received, they can be combined together at the receiver to obtain a reconstruction of the source at a certain quality. If only one of the two descriptions is correctly received, a reconstruction of the source is still possible but at a lower quality. The comparison between the strategies is based on the normalized expected distortion at the receiver, evaluated as a function of outage probability. The results show that the SM strategy achieves the lowest distortion, but in general at the expense of high complexity. It is also shown that the ALM strategy, while being much lower in complexity, is able to achieve performance almost equivalent to SM. We finally consider the outage rates and show that, for each given strategy, the outage probability required for maximizing outage rate is different from the outage probability required for minimizing distortion at the receiver. This implies that the maximization of the outage rate might not be the optimal criterion for the design of a system, since in general it will not lead to the minimization of the distortion at the receiver. II. STRATEGIES FOR I NFORMATION TRANSMISSION A. System Model The system considered in this work is the 2×2 MIMO system of Fig. 1. It is characterized by the channel matrix H, which has the form H =  h 11 h 12 h 21 h 22  Each entry h ij of the channel matrix H represents the gain of the channel between j -th transmit antenna and i-th receive antenna. Each one of these channels is assumed to be indepen- dent, random and with very slow Rayleigh fading. The h ij are then i.i.d. complex Gaussian random variables with zero mean and unit variance, which remain constant over the transmission of a large number of symbols.