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Channel Matched Source Quantization

Errors in the received frame are both due to the quantization and channel errors. At high bit error rates, pe, a high rate quantizer is more sensitive to the channel errors [6]. This causes many received blocks of data to be in error. Therefore, by adjusting the quantization rate to match the channel bit error rate error-resilience can be achieved. The quantization rate can be varied by multiplying each entry in the quantization table by a quantizer factor, say, M. When a coarse quantizer is used by increasing the quantizer factor, M, for a given pe the errors in the received signal reduce. It reaches a minimum for the optimal choice, namely, M*. If the bit rate is reduced further then the quantization errors contribute significantly to the degradation in the received signal. The number of blocks in error increases again. Hence, it is necessary to compute the optimal quantization parameter for the channel limited or quantizer limited region. In other words, if X denotes the source video frame, U is the quantized frame and V is the received frame, then the reconstruction error variance for transmission over a noisy channel is given by

The quantities $\sigma_q^2$, $\sigma_c^2$ and $\sigma_m^2$ denote the quantization, channel and the mutual error variance. The contribution of $\sigma_m^2$ can be neglected for a small bit error probability. However, we account for this in our simulations. Under noise free conditions the quantization error variance is minimized using the perceptually-optimized quantization values given in Figure 3. When the channel is noisy, $\sigma_c^2$is minimized by a proper choice of the quantizer parameter, M. Therefore, $\sigma_{rec}^2$ is minimized by the optimal choice of M. Thus, the optimal value M* is a function of $\sigma_q^2$ and $\sigma_c^2$ as shown in Figure 4. Computing a closed form solution for M* may not be possible due to the presence of VLC. Therefore, we resort to simulative methods.


 
Figure 5:   Q-C curve for pe=10-1
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Figure 6:   Q-C curve for pe=10-2
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Figure 7:   Q-C curve for pe=10-3
\begin{figure} \vspace{0.3in} \centerline{ \psfig {figure=curvefitted3.eps,height=3in,width=4in} } \vspace{0.06in} {\bf } \vspace{0.1in}\end{figure}


 
Table I: Look-up table for M*
pe M*
10-1 2
10-2 1.3
10-3 1
 


 
Figure 8:   Quantized video frame for p2=10-2
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