MINIMUM VARIANCE MULTIPLEXING OF MULTIMEDIA OBJECTS G. Valenzise, M. Tagliasacchi, S. Tubaro Dipartimento di Elettronica e Informazione Politecnico di Milano P.zza Leonardo da Vinci, 32 20133 - Milano, Italy Email: {valenzise, tagliasa, tubaro}@elet.polimi.it ABSTRACT This paper addresses the problem of simultaneous transmission of multiple multimedia objects (such as images or video sequences) over a bandwidth-limited channel. The trivial strategy of partition- ing in equal parts the available rate among the bitstreams is subop- timal, when the multimedia objects have different coding complexi- ties. Exploiting object diversity allows us to allocate the bandwidth according to some optimality criteria, e.g. minimizing the average total distortion or minimizing the variance between the distortions of each object. By describing the rate-distortion characteristics of each multimedia object in terms of a simple exponential model, we pro- vide a closed form solution for both the minimum average and the minimum variance problems. In addition, if we consider the statisti- cal distribution of the rate-distortion model parameters, we can show that the minimum variance solution can effectively reduce the qual- ity fluctuations among the objects, with an overall coding efficiency loss, w.r.t. the minimum average solution, of only 0.5dB on aver- age. Some experiments, carried out on different H.264/AVC video sequences, validate our theoretical results. Index Terms— Multimedia, coding, statistical multiplexing, rate control 1. INTRODUCTION The simultaneous transmission of multiple multimedia data streams on the same bandwidth-limited channel is a very common problem in many practical applications, ranging from broadcast television to video and signal-based surveillance systems. A common task in these applications is how to allocate the available bandwidth to each multimedia object in a somehow optimal way. A very simple solution to the problem is to divide the bandwidth among the mul- timedia objects so that each bitstream receives an equal portion of the bit rate. It is straightforward to see that this method is optimal only in the case that all the multiplexed objects share the same rate- distortion characteristics. In practice this is rarely the case and more sophisticated bit allocation techniques have to be considered. The problem of distributing the available bandwidth across the objects has been addressed in the literature under the name of statis- tical multiplexing [1]. The term was first used to indicate the joint transmission of multiple objects on the same channel: due to the different coding complexities of each multimedia object, an approx- imately constant bit rate channel results from multiplexing several data sequences. The diversity of the multiplexed multimedia objects can be further used to allocate the bit rate according to some opti- mality criteria, e.g. to minimize the average object distortion (MI- NAVE) or the variance of the object distortions (MINVAR) under some rate constraint. Previous works in the literature have concen- trated in particular on the first task [2][3], while for the second there are some specific works [4][5] which deal with the minimization of quality fluctuations of the objects along time, for the case of video sequences. In [6], a joint rate control for multiple H.264/AVC video sequences is proposed, which uses a look-ahead processing window to allocate the bandwidth resources in order to reduce quality varia- tions along time. A different technique which yields similar results is presented in [7]. In both these two works, it is shown that by reducing the quality variations along time, also the differences in distortion between multimedia objects are kept small. In a previous work [8], the authors have shown that it is possible to achieve the same distortion for the multiplexed objects in an effi- cient way, for the case of video sequences, using the ρ-domain model proposed in [9]. In this paper, we extend the solution to the MIN- VAR problem for multimedia objects whose rate-distortion charac- teristics can be described by a simple exponential model. The goal is to achieve constant quality among the different objects meeting a total rate constraint. Our contribution is novel in the following as- pects: first, we find a closed form solution to the MINVAR problem, which holds for those multimedia data whose rate-distortion char- acteristics can be approximated by the exponential model. Second, we provide a statistical analysis of the performance of the MINVAR solution w.r.t. the MINAVE optimization: we show that, even if the average distortion attained by MINAVE solution is better, the MINVAR distortion in terms of PSNR is only 0.5 dB worse on av- erage. Although our method applies to a broad range of multimedia objects, as a proof of concept we illustrate the results multiplexing some H.264/AVC video sequences in Section 5. The rest of the paper is organized as follows: Section 2 describes and justifies the expo- nential rate-distortion model adopted in the rest of the paper; Section 3 presents the MINAVE and MINVAR closed form solutions; Sec- tion 4 compares the distortion obtained solving the MINVAR prob- lem with the minimum average distortion; Section 5 illustrates an example where objects are video sequences; finally, Section 6 draws the conclusions. 2. RATE-DISTORTION MODEL We consider here multimedia objects whose rate R and distortion D are related by the following exponential model: D(R)= σ 2 e - R β , (1) where σ 2 is the variance of the object data and β is a parameter re- lated to the coding complexity of the multimedia data. Given two objects with the same variance σ 2 , we need to spend more bits to encode the object with the higher value of β in order to attain the 1133 1-4244-1484-9/08/$25.00 ©2008 IEEE ICASSP 2008