Consider a random variable X which takes values in X= (1, 2, 7) with probabilities as the following table indicates. Consider the two codes wi and w2 defined by the table below X₁ P(X) WI(x) 12(x) X₁ 0.08 1001 010 X₂ 0.21 01 011 X3 0.14 001 000 X₁ 0.04 1000 110 ii. The average codeword length for each code. L(wi) bit/symbol Xs 0.25 11 111 Answer the following: i. Express (into original symbols Xi) the encoded string (000011010111101} using code wi(x). L(w2) bit/symbol X6 0.11 iii. Explain which code is better for compression applications, and why? 000 101 X1 0.17 101 001

Consider a random variable X which takes values in X= (1, 2, 7) with probabilities as the following table indicates. Consider the two codes wi and w2 defined by the table below X₁ P(X) WI(x) 12(x) X₁ 0.08 1001 010 X₂ 0.21 01 011 X3 0.14 001 000 X₁ 0.04 1000 110 ii. The average codeword length for each code. L(wi) bit/symbol Xs 0.25 11 111 Answer the following: i. Express (into original symbols Xi) the encoded string (000011010111101} using code wi(x). L(w2) bit/symbol X6 0.11 iii. Explain which code is better for compression applications, and why? 000 101 X1 0.17 101 001

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

5
Consider a random variable X which takes values in X= {1, 2, 7} with probabilities as the
following table indicates. Consider the two codes wi and w2 defined by the table below
X₁
P(X)
wi(x)
w2(x)
X₁
0.08
1001
010
X₂
0.21
01
011
X3
0.14
001
000
X₁
0.04
1000
110
ii. The average codeword length for each code.
L(wi) bit/symbol
Xs
0.25
11
111
Answer the following:
i. Express (into original symbols Xi) the encoded string {000011010111101} using code
wi(x).
L(w2) bit/symbol
X6
0.11
000
101
iii. Explain which code is better for compression applications, and why?
X1
0.17
101
001

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