Q-C Modeling

A model that relates the number of block errors in the reconstructed frame and M is developed in this section. The parameters of the model are computed using extensive simulations for bit error rates ranging from 10^-3 to 10^-1. The channel is assumed to cause random bit errors. We call the quantizer-channel error trade-off as the Q-C curve [11]. The rate of the quantizer can be adapted to the channel bit error rate by suitably changing M. The value of M is increased in steps of 0.2 for a fixed p_e and the number of significantly corrupted reconstructed blocks are computed. The higher the value of M the coarser is the quantization. The I-frames are assumed to be sufficiently protected from channel errors and there are 30 P-frames between any two I-frames. The successive received frames are reconstructed from the nearest I-frame after motion compensation. A 8$\times$8 reconstructed image block is termed erroneous if the peak signal to noise ratio (PSNR) of the reconstructed block defined as

$$PSNR = 10\log_{10}\left(\frac{255^{2}}{\frac{1}{N^2}\display... ...N-1} \displaystyle\sum_{j=0}^{j=N-1}(X(i,j)-V(i,j))^{2}}\right)$$ (1)

is less than 30 dB. The Q-C curve is the average number of erroneous blocks averaged over a number of video frames and sequences for various values of M. This produces a Q-C curve for that p_e. The same procedure is repeated for other channel bit error rates also. The experimental Q-C curves (non-smooth) are shown in Figure 5, 6 and 7. A second order regression model for the average number of blocks in error is fitted to the experimental results shown as the solid curve. The optimal value of the quantizer factor, M^* minimizes the average number of blocks in error in the regression model. The optimal quantizer values are given in Table I. For example Figure 8(a) and Figure 8(b) shows the received frame for p_e=10^-2 for two different quantizers. We see that using the value of M^* from Table I for this bit error rate results in a reduction in the total number of corrupted blocks. A similar performance improvement is seen for other bit error rates also.

 

Figure 9:   Schematic of stochastic learning automaton