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Let us consider a binary symmetric channel, as shown in Figure 1, where the probabilities of the input X are Pr(X-0] =...
Question 1) Consider the following Cascade of two Binary symmetric channels (CBSC) with probabilities as indicated in the figure below 1. Find P(Y=1 / X=1 ), P(Y=0 / X=1) 2. Find P(Y=1 / X=0 ), P(Y=0...
Question 1)
Consider the following Cascade of two Binary symmetric
channels (CBSC) with probabilities as indicated in the
figure below
1. Find P(Y=1 / X=1 ), P(Y=0 / X=1)
2. Find P(Y=1 / X=0 ), P(Y=0 / X=0)
3. Find The Channel Matrix for
each BSC separately
4. Find The overall
Channel Matrix of the cascade channels
5. Assume that P1 = P2 =
Pe , Prove that the Channel Matrix is
M2
6. Use the assumptions and results in...
Consider a binary erasure channel, in which the input X ∼ Bernoulli ? (1 ?, 3)...
Consider a binary erasure channel, in which the input X ∼
Bernoulli ? (1 ?,
3)
and the output Y ∈ {0, e, 1} where the symbol e denotes an
erasure event (e appears when the channel is too “bad”). The
conditional distribution of Y given X is as follows:
pY |X (0|0) = 0.9, pY |X (e|0) = 0.1, pY |X (1|1) = 0.8, pY |X
(e|1) = 0.2.
Given that an erased symbol has been observed, i.e., Y...
Exercise 1 Assume that a binary symmetric channel is used in this question as shown in fig. 1 I-p...
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Exercise 1 Assume that a binary symmetric channel is used in this question as shown in fig. 1 I-p 0 0 Alice (encoder) Bob (decoder) 1 1-P Figure 1 The Binary symmetric channel where the probability of a bit being wrongly decoded by Bob is p i) Two codes are proposed: a...
Information bits {0,1} are sent over binary symmetric communication channel with conditional probabilities P(YX) as shown...
Information bits {0,1} are sent over binary symmetric communication channel with conditional probabilities P(YX) as shown below. The priory probabilities of 0 and 1 are P(X=0)=0.3, P(X=1)=0.7. The error probability {=0.2. transmitter X 0 1-€ receiver Y 0 ៩ w 1-€ a) If 1 is transmitted, what are the probabilities of receiving 0 and 1? P(Y=0|X=1) and P(Y=1X=1) b) If 0 is received, what are the probabilities that 0 and 1 information bit is transmitted? P(X=0 Y=0) and P(X=1 Y=0)
Problem 2 - Information Theory Consider the following channel X, DI . a) Calculate entropy of...
Problem 2 - Information Theory Consider the following channel X, DI . a) Calculate entropy of X, i.e., H(X) when [p(31),p(32) = (0.6,0.4). Give p(x1) and p(x2) that maximize H(X) and the corresponding maximum value of H(X). . b) Give the matrix of transition probabilities p(YX)). . c) Calculate output probabilities (p(Y)). . d) Give output probabilities so that H(Y) is maximum. For this case, then give equations with which you can calculate p(x) and p(x2). The SNR is 20...
5. A binary Z-channel is show in the figure. Assume the input is "0" with probability...
5. A binary Z-channel is show in the figure. Assume the input is "0" with probability p and "1" with probability 1-p. (a) What can you say about the input bit if " is received? (b) Find the the probability that the input was "1" given that the output is "0" 0 Input Output 6. A transmitter randomly sends one of the messages in fa1, a2,.. ,an). The receiver either receives the transmitted message with probability p, or mistakenly receives...
Suppose that we are given the following communication system described in Fig. 1 with the channel...
Suppose that we are given the following communication system described in Fig. 1 with the channel corrupted by an additive white Gaussian noise z with zero mean and variance 1 where the channel input.x is used for signal transmission to produce the channel output y,i.e., r- x . Then the channel is further passed through a hard limiter, i.e., sign detector described by Q2(r) in Fig.2 decisions 22(r) Figure 1. A channel with the input x and output r corrupted...
1. Consider sequence of independent identically distributed binary random variable x,,x,,x,,x,-4 ...
1. Consider sequence of independent identically distributed binary random variable x,,x,,x,,x,-4 , wherepEPr(X:-)-0.7 and Pr(X, =0).1-p=0.3. a) (10 pts.) Complete the table where k denotes the number of 1's in the n! sequence, andkkn-k b) (10 pts.) Calculate H(X) c) (10 pts.) Assume that Pr[T)]21-ε 0.9. Find the corresponding typical sequence set n) d) (10 pts.) Assume Pr[ 21-820.9. Find the corresponding smallest set B ). 2. Consider a random walk random variable X, on the graph in Figure 1....
7. The input U of binary communication channel is either -2.5 or +2.5 representing bit values...
7. The input U of binary communication channel is either -2.5 or +2.5 representing bit values b = 0 and b = 1 respectively, where P(b = 1) = 0.75. The channel output is given by V = U+N where “channel noise” N is a continuous random variable whose pdf is a symmetric triangular function in the range (-3, +3). Assume that U and N are independent. The receiver decodes the channel output to produces a bit value b as...
1. Consider the Probability distributions shown in Figure below, where the signal voltage for binary 1...
1. Consider the Probability distributions shown in Figure below, where the signal voltage for binary 1 is V1 and Vih-V12 1 level o(n Threshold vohage 0 level Additive noiac,y P(y|の a) If σ-0.20 y for p(y/0) and σ-0.24 Vi for p(y/1), find the error probabilities Po(Vh) and Pi(Vth) b) If a-0.65 and b-0.35, find Pe c) If a-b-0.5, find Pe
Question 1)
Consider the following Cascade of two Binary symmetric
channels (CBSC) with probabilities as indicated in the
figure below
1. Find P(Y=1 / X=1 ), P(Y=0 / X=1)
2. Find P(Y=1 / X=0 ), P(Y=0 / X=0)
3. Find The Channel Matrix for
each BSC separately
4. Find The overall
Channel Matrix of the cascade channels
5. Assume that P1 = P2 =
Pe , Prove that the Channel Matrix is
M2
6. Use the assumptions and results in...
Consider a binary erasure channel, in which the input X ∼
Bernoulli ? (1 ?,
3)
and the output Y ∈ {0, e, 1} where the symbol e denotes an
erasure event (e appears when the channel is too “bad”). The
conditional distribution of Y given X is as follows:
pY |X (0|0) = 0.9, pY |X (e|0) = 0.1, pY |X (1|1) = 0.8, pY |X
(e|1) = 0.2.
Given that an erased symbol has been observed, i.e., Y...
I need it urgently. Kindly provide me in neat and clean. Thanks
in advance.
This information is complete and if You think info is incomplete
than kindly mention.
Exercise 1 Assume that a binary symmetric channel is used in this question as shown in fig. 1 I-p 0 0 Alice (encoder) Bob (decoder) 1 1-P Figure 1 The Binary symmetric channel where the probability of a bit being wrongly decoded by Bob is p i) Two codes are proposed: a...
Information bits {0,1} are sent over binary symmetric communication channel with conditional probabilities P(YX) as shown below. The priory probabilities of 0 and 1 are P(X=0)=0.3, P(X=1)=0.7. The error probability {=0.2. transmitter X 0 1-€ receiver Y 0 ៩ w 1-€ a) If 1 is transmitted, what are the probabilities of receiving 0 and 1? P(Y=0|X=1) and P(Y=1X=1) b) If 0 is received, what are the probabilities that 0 and 1 information bit is transmitted? P(X=0 Y=0) and P(X=1 Y=0)
Problem 2 - Information Theory Consider the following channel X, DI . a) Calculate entropy of X, i.e., H(X) when [p(31),p(32) = (0.6,0.4). Give p(x1) and p(x2) that maximize H(X) and the corresponding maximum value of H(X). . b) Give the matrix of transition probabilities p(YX)). . c) Calculate output probabilities (p(Y)). . d) Give output probabilities so that H(Y) is maximum. For this case, then give equations with which you can calculate p(x) and p(x2). The SNR is 20...
5. A binary Z-channel is show in the figure. Assume the input is "0" with probability p and "1" with probability 1-p. (a) What can you say about the input bit if " is received? (b) Find the the probability that the input was "1" given that the output is "0" 0 Input Output 6. A transmitter randomly sends one of the messages in fa1, a2,.. ,an). The receiver either receives the transmitted message with probability p, or mistakenly receives...
Suppose that we are given the following communication system described in Fig. 1 with the channel corrupted by an additive white Gaussian noise z with zero mean and variance 1 where the channel input.x is used for signal transmission to produce the channel output y,i.e., r- x . Then the channel is further passed through a hard limiter, i.e., sign detector described by Q2(r) in Fig.2 decisions 22(r) Figure 1. A channel with the input x and output r corrupted...
1. Consider sequence of independent identically distributed binary random variable x,,x,,x,,x,-4 , wherepEPr(X:-)-0.7 and Pr(X, =0).1-p=0.3. a) (10 pts.) Complete the table where k denotes the number of 1's in the n! sequence, andkkn-k b) (10 pts.) Calculate H(X) c) (10 pts.) Assume that Pr[T)]21-ε 0.9. Find the corresponding typical sequence set n) d) (10 pts.) Assume Pr[ 21-820.9. Find the corresponding smallest set B ). 2. Consider a random walk random variable X, on the graph in Figure 1....
7. The input U of binary communication channel is either -2.5 or +2.5 representing bit values b = 0 and b = 1 respectively, where P(b = 1) = 0.75. The channel output is given by V = U+N where “channel noise” N is a continuous random variable whose pdf is a symmetric triangular function in the range (-3, +3). Assume that U and N are independent. The receiver decodes the channel output to produces a bit value b as...
1. Consider the Probability distributions shown in Figure below, where the signal voltage for binary 1 is V1 and Vih-V12 1 level o(n Threshold vohage 0 level Additive noiac,y P(y|の a) If σ-0.20 y for p(y/0) and σ-0.24 Vi for p(y/1), find the error probabilities Po(Vh) and Pi(Vth) b) If a-0.65 and b-0.35, find Pe c) If a-b-0.5, find Pe
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