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ARIZONA STATE UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
EEE 508
Spring 2015
Problem Set #5
Assigned: 2 April 2015
Due Date: 16 April 2015
Reading: Finiah reading the Lossless Coding material placed on Blackboard. Start reading the
Coding Material (JPEG, JPEG2000, H.264AVC) placed on Blackboard.
PROBLEM 5.1:
(3 points)
Consider the application of DPCM to an image as suggested by the figure shown below.
C
B
j
j
D
j
A
j
We will base our prediction of pixel A on pixels B, C, D.
Assume that the correlation between pixels is known and given by
ρAB = ρBD = ρCD = ρAC = ρ
0
ρAD = ρBC = ρ
Following our discussion in class, what are the optimal fixed predictors (B, C, D) for this 2-D DPCM
system ?
PROBLEM 5.2:
(4 points) Consider a random source S which produces the output symbols s1 with probability
P1 = 0.25, s2 with probability P2 = 0.5, and s3 with probability P3 = 0.25.
(a) (1 point) Determine the first-order entropy of the source S.
(b) (1.5 points) If Huffman coding is used, determine the codewords assigned to each symbol and
the resulting average bit-rate. Justify your answer.
(c) (1.5 points) If Arithmetic coding is used, determine the codeword that can be used to code
the sequence of symbols {s2 , s3 , s1 }. Justify your answer.
PROBLEM 5.3:
(3 points) Consider the following 8 × 8 image x(n1 , n2 ) corresponding to the (n − 1) frame of a
video sequence:
(
2, 2 ≤ n1 , n2 ≤ 5
x(n1 , n2 ) =
1, otherwise
Consider also the following associated motion vectors corresponding to each 2×2 block (i, j), where
(i, j) = (0, 0) corresponds to top left block and (i, j) = (3,3) corresponds to bottom right block:
(
M V (i, j) =
[1, 1], 1 ≤ i, j ≤ 2
[0, 0], otherwise
(a) (2 points) Using the motion vectors above, construct the motion compensated image for frame
n.
(b) (1 point) Consider a video sequence with frame size 512 × 512 pixels. If motion blocks of
16 × 16 are used, how many motion vectors must be transmitted as side information?