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2. Consider a binary communication channel The probability that a transmitted 0 is received as 1 ...
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...
A 2-bit binary sequence is transmitted over a noisy communication channel. The noise corrupts the signal...
A 2-bit binary sequence is transmitted over a noisy communication channel. The noise corrupts the signal in the sense that a transmitted digit transmitted can be flipped with probability 0.1. It has been observed that, across a large number of transmitted signals, the 0s and 1s are transmitted in the ratio 3:4. Given that the sequence 01 is received, calculate the probability that this sequence was transmitted.
Consider a binary communication channel transmitting coded words of n bits each. Assume that the probability...
Consider a binary communication channel transmitting coded words of n bits each. Assume that the probability of successful transmission of a single bit is p (and the probability of an error is q=1-p), and that the code is capable of correcting up to e (where e>= 0) errors. If we assume that the transmission of successive bits is independent, then what is the probability of successful word transmission? Hint: the word is successfully transmitted if there are e or fewer...
Consider a binary modulation scheme in which the transmitted signals are 81-0 and s2=A with prior...
Consider a binary modulation scheme in which the transmitted signals are 81-0 and s2=A with prior probabilities P the received signal is p and P2 1-p. These signals are sent over an AWGN channel and r=si + n for i = 1,2 where n is a Gaussian noise with zero mean and variance No/2. a) Determine the MAP decision regions for this signaling b) Express the error probability in terms of Q-functions.
Consider a binary modulation scheme in which the...
Let us consider a binary symmetric channel, as shown in Figure 1, where the probabilities of the input X are Pr(X-0] =...
Let us consider a binary symmetric channel, as shown in Figure 1, where the probabilities of the input X are Pr(X-0] = m and Pr(X-1-1-m, and the error probability during the transmission from X and Y is p. 0 1-p Figure 1: A typical binary symmetric channel, where the input is X and the output is Y. a) Given that p-1/3 and m-3/4, find H(X), H (Y), H (YİX), and 1(X:Y). (8 marks) b) Still given p = 1 /3....
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...
m variable X takes its two In a binary communication system the transmitted rando values (1,2) with equal probability, and the received random variable Y has conditional pdís given by frx(1)-1) and r...
m variable X takes its two In a binary communication system the transmitted rando values (1,2) with equal probability, and the received random variable Y has conditional pdís given by frx(1)-1) and rnx(u 12)I1). a) Draw the two pdfs on the same coordinate system. b) Find the optimal decision rule for guessing the transmitted value of X. c) Find the probability of error of the optimal decision rule.
m variable X takes its two In a binary communication system the...
randi (Lo), 1000, Lab Description In this lab, you are to simulate a simple binary communication...
randi (Lo), 1000, Lab Description In this lab, you are to simulate a simple binary communication channel characterized by appropriate conditional and prior probabilities and estimate the probability of error as well as the probability of receiving either a 1 or a 0. Start with a symmetrie binary communication channel characterized by the conditional probabiliti PLRlis 0.995 and POR I PR 0.003 The prior prebabilities of a 0 or a l are given by POs)-0.389 a PI ls 0.6 Xi...
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...
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)
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...
Consider a binary modulation scheme in which the transmitted signals are 81-0 and s2=A with prior probabilities P the received signal is p and P2 1-p. These signals are sent over an AWGN channel and r=si + n for i = 1,2 where n is a Gaussian noise with zero mean and variance No/2. a) Determine the MAP decision regions for this signaling b) Express the error probability in terms of Q-functions.
Consider a binary modulation scheme in which the...
Let us consider a binary symmetric channel, as shown in Figure 1, where the probabilities of the input X are Pr(X-0] = m and Pr(X-1-1-m, and the error probability during the transmission from X and Y is p. 0 1-p Figure 1: A typical binary symmetric channel, where the input is X and the output is Y. a) Given that p-1/3 and m-3/4, find H(X), H (Y), H (YİX), and 1(X:Y). (8 marks) b) Still given p = 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...
m variable X takes its two In a binary communication system the transmitted rando values (1,2) with equal probability, and the received random variable Y has conditional pdís given by frx(1)-1) and rnx(u 12)I1). a) Draw the two pdfs on the same coordinate system. b) Find the optimal decision rule for guessing the transmitted value of X. c) Find the probability of error of the optimal decision rule.
m variable X takes its two In a binary communication system the...
randi (Lo), 1000, Lab Description In this lab, you are to simulate a simple binary communication channel characterized by appropriate conditional and prior probabilities and estimate the probability of error as well as the probability of receiving either a 1 or a 0. Start with a symmetrie binary communication channel characterized by the conditional probabiliti PLRlis 0.995 and POR I PR 0.003 The prior prebabilities of a 0 or a l are given by POs)-0.389 a PI ls 0.6 Xi...
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...
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)
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