A remote color sensor observes a color manufacturing process and transmits observations to a control center. The observed colors occur with the following probabilities:
P (Red) = 3/4
P (Green) = 1/8
P (Blue) = 1/16
P (Yellow) = 1/16
A computer at the sensor encodes the color observations according to the following code:
Red ? 00
Green ? 01
Blue ? 10
Yellow ? 11
These codewords are then sent to the control center (leftmost bit first).
a. What is the average length of the code?
b. The sequence (0000000100000011000000000000 0100) was received at the control center with the leftmost bit received first. What is the observed sequence of colors?
c. Notice that the observed sequence from part b is highly redundant. To reduce this redundancy, devise a code that has an average length less than two. What is the average length of your code?
d. Encode the following sequence of color observations (leftmost observed first) with your code from part c: {Red, Red, Red, Green, Red, Red, Red, Yellow, Red, Red, Red, Red, Red, Red, Green, Red}. Do you see an improvement?
Analysis:
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