Consider a predictive coding system that predicts the current sample using the previously reconstructed

sample; and the prediction error $($e$)$ is quantized according to:

$Q(e)=\{\begin{array}{cc}2,& e0\\ -2,& e<mn\; id="EditorElement\_220343">0</mn>\end{array}$

$3\mathrm{.}1$ For the pixel sequence $\{3,4,5,3,1,$dots$\}$

Show the predicted value, the prediction error, the quantized prediction error, and the reconstructed value,

for each sample, starting from the first sample. Assume that the encoder and decoder will use the value of

$2$ as the prediction value for the first sample.

$3\mathrm{.}2$ Assuming $"1"$ represent $e0."0"$ for also write the binary representation of the coded stream.

What is the bit rate of the coded stream? $($in terms of bit$/$sample$)$