1. For P(a1)=0.2, P(a2)=0.3, P(a3)=0.5, find the real tag for the sequence {a1, a1, a3, a2, a3 , a1} using arithmetic coding.
2. For P(a1)=0.2, P(a2)=0.3, P(a3)=0.5, decode sequence of length 10 with tag 0.63215699.
3. Given an initial dictionary consisting of the letters a, b, r, y, _, encode the following message using LZW algorithm:
a_bar_array_by_barrayar_bay
4. a. Use 1-st order DPCM to encode the sequence 10 11 12 11 12 13 12 11
b. Use the 1-st order DPCM to encode the sequence 10 -10 8 -7 8 -8 7 -7
Find a better predictor for this sequence and perform the DPCM again.
5. Calculate the 2-D 4x4 DCT of the image block as shown [1 2 3 4; 2 3 4 3; 3 4 3 2; 4 3 2 1] (matrix)