Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 16.3, Problem 9E
Program Plan Intro
To show that no compression scheme can expect to compress file of randomly chosen 8-bit characters by even a single bit.
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Give the result of encoding the strings ab, abab, ababab, abababab, ... (stringsconsisting of N repetitions of ab) with run-length, Huffman, and LZW encoding. Whatis the compression ratio as a function of N?
4. Given a sentence
JALESVEVA JAYAMAHE
a. Create a frequency table for each letter or character (including blank,
distinguish between uppercase and lowercase letters).
b. If 1 letter takes 1 byte (8 bits) of memory, how many bytes is it?
the memory required to store the text?
c. Apply Huffman coding algorithm, to summarize
(compress) the sentence.
d. What is the summarization efficiency (what % of memory saving is
generated)?|
Let æ(n1, n2) represent an 8x8 luminance block. The DCT of r(n1, n2) is quantized using
the JPEG luminance quantization Q matrix as specified in Section K, Table K.1, of the ISO/ITU-T
JPEG standard document that is provided on the course web site. The resulting quantized DCT
of a(n1, n2) is given by:
128 10 0
...
-4 0
...
X4(K1, K2) =
0.
...
0 0
...
which contains only three non-zero coefficients.
(a) Using Table F.2 (page 90) and Table K.5 (pages 150 to 153) of the ISO/ITU-T JPEG standard
document that is provided on the course web site, determine the JPEG bit stream for the AC
coefficients.
(b) What is the average bit-rate associated with these coded AC coefficients (in bits/coefficient)?
(c) What is the JPEG bit-stream of the considered 8 x 8 block if the quantization Q matrix is a
constant matrix where each element is equal to 3000?
Chapter 16 Solutions
Introduction to Algorithms
Ch. 16.1 - Prob. 1ECh. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - Prob. 5ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5E
Ch. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5P
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