## 4 Simulation Results and Discussion
Let us now focus on the computational complexity of the proposed technique, by analyzing the number of operations performed by the MS for the QoS assessment. According to Fig. 2, the floating point operations (flops) to be implemented by the MS processor are: first, the computation of the \(k_{I}\)-by-\(k_{2}\) DCT of each frame; second, the correlation with the spread version of the watermark made of \(\lambda k_{I}k_{2}\) pixels (_i.e._ the original watermark pre-multiplied by one known PN matrix, different frame by frame); third, the accumulation of the detected mark averaged over \(M\) frames; last, the final evaluation of the MSE of the detected mark at the end of the procedure. The whole computation can be implemented either by sequential or parallel processing, depending on the available hardware. The approximate computing time needed by the QoS assessment procedure (from \(M\) frames of \(k_{I}\) by \(k_{2}\) pixels) operating either on sequential or parallel processors on a mobile device is depicted in Table. 1, in terms of the time required by the number of flops. For sake of compactness, we have reported only the number of real products and sums, assuming that:  
- in sequential implementation, the time of one complex product is the same as four real products and two real sums, whereas the time of one complex sum time is equivalent to two real sums;  
- in parallel implementation, the time of one complex product is the same as one real product and one real sum, whereas the time of one complex sum time is equivalent to one real sum. It has to be noted that in all the aforementioned cases, the DCT computation is the most time-consuming step: 98.8% of operations for sequential implementation and 92.2% for parallel implementation are required for the only DCT processing over the whole computation time. The tremendous advantage of parallel computing is motivated by the fact that DCT computation is implemented by fast Fourier transform (FFT). In fact, the computational complexity of FFT (over \(N\) data) is of the order of \(N\)\(log_{2}\)\(N\), whereas it reduces to the order of \(log_{2}\)\(N\) by parallel processing schemes. It is opinion of the authors that the implementation of the proposed technique is going to be feasible on a mobile device as the MS, in a short time, will host large processing capabilities (including hardware DCT co-processors) because of the monotonically decreasing cost of very large-scale  
\begin{table}
\begin{tabular}{l c c c c}  & Sequential processing & & Parallel processing \\  & No of real products & No of real sums & No of real products & No of real sums \\ \hline DCT & \(8M\)\(k_{1}\)\(k_{2}\)\(\log_{2}(4k_{1}k_{2})\) & \(8M\)\(k_{1}k_{2}\)\(\log_{2}(4k_{1}k_{2})\) & \(M\)\(\left[\log_{2}(2k_{1})+\log_{2}(2k_{2})\right]\) & \(2\)\(M\)\(\integration as well as the ever increasing running speed. Therefore the complexity of the QoS evaluation procedure, which is presented in this paper, appears negligible in comparison with real-time MPEG decoding and adaptive on-board array processing. The obtained results prove the sensitivity of the watermarking quality index to the actual quality for given target quality levels and show the capability of this network-aware processing of multimedia content to trace the alterations suffered by the data through the network. Hence, the advantages of distributing the management process can be summarized in: (i) an easier and more precise localization of the cause of QoS problems, (ii) better knowledge of local situations, (iii) a lower complexity for a single QoS agent and (iv) an increase in possible actions.