PERFORMANCE OF MULTIPLE DESCRIPTION CODING IN SENSOR NETWORKS WITH FINITE BUFFERS E. Baccaglini Dip. di Elettronica - Politecnico di Torino Ist. Sup. M. Boella - Multimedia Networking Lab 10129 Torino, Italy enrico.baccaglini@polito.it G. Barrenetxea, B. Beferull-Lozano Lab. de Communications Audiovisuelles Ecole Polytechnique Federale de Lausanne CH-1015 Lausanne, Switzerland {guillermo.barrenetxea, baltasar.beferull}@epfl.ch ABSTRACT Sensor networks are usually dense networks where the network diversity can be exploited in order to overcome failures. In this paper, we study the use of multiple description techniques in the context of sensor networks where the cause of failures is due to the usual practical constraint of having finite buffers in the sen- sors, instead of the more traditional case of link failures consid- ered in previous research. Although from a theoretical point of view we observe that the use of more descriptions provides usu- ally better performance, we show experimentally that this is not the case in practice, when real constraints are introduced, such as finite buffers and the presence of header information, necessary for any real application. Our main result is that the optimal num- ber of descriptions, in terms of average distortion, decreases as the fraction of header information increases for a given buffer size. 1. INTRODUCTION Sensor networks are usually composed of a large number of in- dividually-unreliable nodes with many connecting paths between them. Transmissions over these networks are subject to failures such as buffer overflow and node breakdowns resulting in packet losses. This scenario motivates the use of specific coding tech- niques capable of exploiting network diversity in order to face node unreliability. In this paper, we focus our attention on losses caused by the finite buffer capacity of nodes. Common devices used in sensor networks presents a limited and generally small amount of memory [1] that translates into a limited capacity for the temporary storage of packets. This causes dropping when the rate of packets injected is sufficiently high. In some scenarios, retransmission is not possible due to time constraints or expen- sive feedback and so coding schemes that make all of the received packets useful can be of great benefit. Multiple Description (MD) coding applies precisely to this situation. As opposed to Single Description (SD) coding, an MD source encoder partitions infor- mation into descriptions and then sends them over the available paths to the receiver. Depending on the subset of packets that is re- ceived, a side decoder computes an estimate of the original source. The quality of the estimate depends on the number of descriptions received but, in contrast to the single-description case, the loss of packets does not lead to a failure. A generic MD coding schema is shown in Fig. 1 for the case of three descriptions. Several MD coding techniques has been proposed, based on Unequal Error Protection (UEP) [2, 3] and on scalar quantizers CH.1 CH.2 CH.3 Source ENC D2 D3 D1 D12 D13 D23 DC Fig. 1. A MD system with three descriptions. Central decoder DC receives all the descriptions and can reconstruct the finest repre- sentation of the source. The other decoders receive only a subset of the transmitted data. (MDSQ) [4]. However, in all this previous work, only the two- description case is addressed and the interaction between the net- work conditions and the different practical aspects of building MD codes has not been studied. In this paper, we start by studying the dependence between the number of descriptions and the end-to- end distortion for a point-to-point link and a given fixed proba- bility of failure, using both UEP and MDSQ based techniques. Then, we analyze the application of these coding techniques in a sensor network performing a data-gathering task (simultaneous transmissions case) with finite buffers. We analyze the optimal transmission strategy as a function of practical parameters such as packet sizes and transmission rates in addition to the number of descriptions. Although from a theoretical point of view, the use of more descriptions usually provides a better performance, this is not in general the case when we introduce practical constraints (finite buffers and packets containing both header information and payload). Since the presence of the header information (source, destination, sequence numbers, etc. . . ) in each packet containing a description increases the traffic generated for the network, it is shown experimentally that there exists an optimal number of de- scriptions that depends on the fraction of header information for each value of probability of packet loss. The rest of the paper is organized as follows: in Section 2, after introducing the model and assumptions, we introduce UEP and MDSQ in a point-to-point channel and in Section 3 we study MD coding in a data-gathering sensor network. 2. MDC IN A POINT-TO-POINT CHANNEL For the analytical study of a MD coding system, we first consider an information source that emits an iid Gaussian signal with zero