TRADE OFF BETWEEN ROBUSTNESS AND R-D PERFORMANCE IN ZERO PADDING MULTIPLE DESCRIPTION ABSTRACT Multiple description coding (MDC) by sequence under- sampling can be implemented by pre- and post-processing, so it can be associated to most standards for image/video communications. Unfortunately, this method suffers from high side distortion when only one description is received. In order to overcome this limitation, over sampling of sequence via zero padding in the DFT domain has been proposed to improve correlation between subsequent samples, so achieving better estimation of the lost description. The price to be paid is a degradation of the performance in case both descriptions are received. In this paper we present analytical results of zero padded MDC, which can help in the selection of the best trade-off between performance and over sampling factor. 1 INTRODUCTION Techniques which enable the creation of multiple descriptions of images or video sequences, by means of pre- and post-processing to standard co-decoders are very attractive; in fact, they allow to exploit a possible spatial diversity to achieve transmission robustness, without substantial modification of wide spread standards. A straightforward method to achieve this goal it to split the data sequence to be encoded into two sub sequences, which are passed on to the standard encoder (e.g. JPEG in case of still images). At the receiver side, the received sub sequences are combined to achieve the full quality image. In case one description is corrupted or lost, it can be estimated from the received one, exploiting the correlation between the two. Therefore, the quality of the decoded data is heavily dependent on the correlation between the descriptions. Over sampling of the original sequence prior to the description generation can help improving the correlation characteristics, and has been proposed in [1], [2]. Clearly enough, the amount of zero padding should be carefully controlled, as an excessive sequence expansion impairs the system performance in case both descriptions * This work has been supported by CERCOM - Center for Multimedia Radio Communications are received. In fact, the information carried by each transmitted bit is decreased, and the rate/distortion characteristics are worsened. In this paper we present analytical results related to the performance of zero padded MDC (ZP-MDC), which can help selecting the best trade off between central and side distortion achieved. 2 ZP-MDC: THEORETICAL ANALYSIS Let us consider N samples T N x x X ] .. [ 1 = of a white Gaussian random process with zero mean and covariance matrix N X I R 2 0 σ = , where N I is the N N × identity matrix. Let us assume that this sequence is zero padded by introducing Z =P-N zeros in the DFT domain. If N T represents the normalized DFT matrix for N samples, the over sampled sequence can be expressed as GX X T I I T Y N N N N Z N Z N N P = ×           × = × × − 2 / 2 / 2 / 2 / 2 / 2 / 1 0 0 0 0 where 2 / 0 N is the N/2 x N/2 null matrix . The covariance matrix Y R of the obtained sequence Y is P N N Z N Z N N Z Z N Z Z N N H P H X H Y T I I T G GR YY E R           = = = = × × × × × 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 0 0 0 0 0 0 0 0 } { σ and the correlation at lag i can be easily worked out as ) / ( ) / ( ) ( 2 0 P i Sin P Ni Sin P i R Y π π σ = corresponding to a correlation coefficient ) / ( ) / ( 1 ) 0 ( ) 1 ( P Sin P N Sin N R R Y Y π π ρ = = (1) Gabriella OLMO * CERCOM Politecnico di TORINO Department of Electronics Corso Duca degli Abruzzi 24 10129 Torino (Italy) gabriella.olmo@polito.it Tammam TILLO * CERCOM Politecnico di TORINO Department of Electronics Corso Duca degli Abruzzi 24 10129 Torino (Italy) tammam.tillo@polito.it