a) Given that p = 1/3 and m = = 3/4, compute H(X), H(Y) and H(Y|X). b) Still given p= 1/3. Compute the capacity of this binary symmetric channel. c) Now consider a new binary channel which consists of two original binary symmetric channels con- nected in series as shown in Figure 2. 1-p 0 X 1 р P P P 1-p +0 Y 1 1-p 1-p Figure 2: A new binary channel given by the series connection of two original and identical binary symmetric channels. The parameter p is still the error probability for transmission over one binary symmetric channel. Given that p = 1/3. Compute the capacity of this new binary channel.
a) Given that p = 1/3 and m = = 3/4, compute H(X), H(Y) and H(Y|X). b) Still given p= 1/3. Compute the capacity of this binary symmetric channel. c) Now consider a new binary channel which consists of two original binary symmetric channels con- nected in series as shown in Figure 2. 1-p 0 X 1 р P P P 1-p +0 Y 1 1-p 1-p Figure 2: A new binary channel given by the series connection of two original and identical binary symmetric channels. The parameter p is still the error probability for transmission over one binary symmetric channel. Given that p = 1/3. Compute the capacity of this new binary channel.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Let us consider a binary symmetric channel, as shown in Figure 1, where the probability distribution
of the input X is given by Pr[X=0] = m and Pr[X = 1] = 1 - m, and the error probability during the
transmission is denoted by p.
1-p
0
0
X
X
р
P
1-p
Figure 1: A typical binary symmetric channel, where the input is X and the output is Y.
р
1
a) Given that p = 1/3 and m = 3/4, compute H(X), H (Y) and H(Y|X).
b) Still given p = 1/3. Compute the capacity of this binary symmetric channel.
0
c) Now consider a new binary channel which consists of two original binary symmetric channels con-
nected in series as shown in Figure 2.
1-p
Y
1
P
P
1-p
0
Y
1-p
1-p
Figure 2: A new binary channel given by the series connection of two original and identical binary symmetric
channels. The parameter p is still the error probability for transmission over one binary symmetric channel.
1
Given that p = 1/3. Compute the capacity of this new binary channel.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6bc6d303-52a6-496d-a490-2e6b9ca359c2%2Fbd872ef7-a00a-437a-84e1-09df340de49e%2Ft15mrk_processed.png&w=3840&q=75)
Transcribed Image Text:Let us consider a binary symmetric channel, as shown in Figure 1, where the probability distribution
of the input X is given by Pr[X=0] = m and Pr[X = 1] = 1 - m, and the error probability during the
transmission is denoted by p.
1-p
0
0
X
X
р
P
1-p
Figure 1: A typical binary symmetric channel, where the input is X and the output is Y.
р
1
a) Given that p = 1/3 and m = 3/4, compute H(X), H (Y) and H(Y|X).
b) Still given p = 1/3. Compute the capacity of this binary symmetric channel.
0
c) Now consider a new binary channel which consists of two original binary symmetric channels con-
nected in series as shown in Figure 2.
1-p
Y
1
P
P
1-p
0
Y
1-p
1-p
Figure 2: A new binary channel given by the series connection of two original and identical binary symmetric
channels. The parameter p is still the error probability for transmission over one binary symmetric channel.
1
Given that p = 1/3. Compute the capacity of this new binary channel.
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