Joint Rate Control and Channel Estimation

Adaptive rate control is one way of achieving error-resilience. For channel matched source rate control the channel bit error probability needs to be estimated first. Transmitting pilot symbols to estimate p_e is a common solution. But, this introduces delay and costs bandwidth. We now discuss a way to overcome this problem by jointly controlling the rate of quantization and on-line estimation of p_e using VSLA. We assume that p_e can take only one of the three values, 10^-1, 10^-2, or 10^-3. At the beginning of the transmission the actual p_e for the channel is unknown. Now, let the set of actions of the automaton, $\alpha=\{\alpha_1,\alpha_2,\alpha_3\}$ correspond to the three channel matched empirically optimal quantizers for channel bit error rates 10^-1, 10^-2, and 10^-3 respectively. Since there is a one-to-one correspondence between quantizers and the channel bit error probability, by learning the optimal quantization parameter we also estimate p_e. Let a favorable response ($\beta=0$)from the decoder for a chosen quantizer imply that the PSNR of the current received video frame is greater than or equal to that of the previous frame and 1 is an unfavorable response. We assume here that PSNR and the number of blocks in error in the received frame are inversely proportional. Therefore, a high PSNR implies fewer number of blocks in error. The penalty probabilities for the choice of each action is unknown and defines the environment (channel's conditions). The goal is to maximize the PSNR of the received video signal by learning the channel condition and choosing the corresponding optimal rate for the source quantizer. This corresponds to learning the action with the minimum penalty probability. The probability of choosing the quantizers are updated using LRI. The typical steps involved in the proposed algorithm are as follows:

• I-frame is quantized using a high rate quantizer and transmitted with sufficient protection.
• The decoder, after reconstructing this frame quantizes it using the the optimal source rates for the three channel bit error probabilities under consideration and stores them in a buffer.
• The VSLA chooses a quantizer randomly for the nth frame with the given probability $\{p_1(n), p_2(n), p_3(n)\}$.
• The quantized is transmitted along with the the quantizer information as protected side information.
• A response $\beta$ based on the PSNR of the decoded frame is transmitted as a feedback information.
• Based on this feedback the probabilities of choosing the quantizers for the n+1st frame is computed using LRI.
• The algorithm learns until the probability of choosing the optimal action for the unknown p_e converges to 1.

When the algorithm converges it has learnt the unknown p_e of the channel by the optimal choice of the quantizer factor. Of course, this method could result in the first few frames to be sub-optimally quantized. This is the cost incurred in on-line channel estimation. However, the learning delay can be controlled by the value of the reward parameter. Depending on the value of the error tolerance $\epsilon$ a suitable reward parameter can be chosen. A higher reward parameter results in faster convergence of the LRI learning. Since p(n) converge w.p.1 let $\lim_{n\rightarrow\infty}\Psi(n)=\Psi^*$ w.p. 1. Then, the average rate of convergence of LRI learning is [21] $\rho_{av}\approx \frac{E[\Psi(n+1)-\Psi^*]}{E[\Psi(n)-\Psi^*]}$.After every frame n, $E[\Psi(n)-\Psi^*]$ decreases by a factor of $\rho_{av}$.If $\tilde{T}$ is the time taken for $E[\Psi(0)-\Psi^*]$ to decrease to d times its value, then $\tilde{T}=logd/log\rho_{av}$For very slowly changing channels, If the channel bit error probability changes then the encoder will receive a series of penalties. Then the learning process can be started again. Therefore, the encoder is in sync with the channel again.

 

Figure 10:   Missamerica sequence, a=0.3

 

Figure 11:   Susie sequence, a=0.3

 

Figure 12:   Claire sequence, a=0.5

 

Figure 13:   Reconstructed Missamerica frames for p_e=10^-1

 

Figure 14:   Reconstructed Missamerica frames for p_e=10^-2