![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 e iss ightlymore ikely than I). О e nput to the binary communication channe isto ea sequence of os and Is. Each 0 or I in the sequence is statistically independent of the others and is generated according to the probabilities P[Os] and P[ls] given above. 1. Generate the data input sequence of Os and 1s according to the required probabilities. 2. Simulate the channel by writing a computer program to do the following: a.) When a 0 is presented as input to the channel, the channel should generate an output of 0 with probability PIOR Os) and an output of 1 with probability PIIROs (where the numerical values are given above). b.) When a 1 is presented to the.channel, the channel should generate a 0 with probability P[OR 1s Repeat the experiment with various lengths of input sequences, Sequence-1-1000 and and a 1 with probability P[IRIS 3. Sequence-2-100,000,000 Compare the results for various length input sequences by tabulating and plotting the %error. 4. In addition, in your lab report answer the following questions: QI: Compute the theoretical values for the following probabilities: POsOR], P[Isl1r] and P[error]. Q2: Explain the length of sequences regarding to the probability of P[error].](http://img.homeworklib.com/questions/47280340-6e29-11ea-ae68-a1520c89eecd.png?x-oss-process=image/resize,w_560)
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randi (Lo), 1000, Lab Description In this lab, you are to simulate a simple binary communication...
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)
2. Consider a binary communication channel The probability that a transmitted 0 is received as 1 ...
2. Consider a binary communication channel The probability that a transmitted 0 is received as 1 is ε1- The probability that a transmitted 1 is received as 0 is Assume that the 2 transmitted inputs have equal probabilities. a) (10 points) Find the probability that the output received is 0. b) (10 points) Find the probability that the transmitted input is 0 given that the received output is 1 e) (5 points) Find the probability that the transmitted input is...
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...
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....
A communication link uses a simple repetition code for error correction, where ain information bit T)"...
A communication link uses a simple repetition code for error correction, where ain information bit T)" is sent by a length-5 sequence of zeros, İ.е., 0 (0,0,0,0,0) Likewise, an information bit "I', is sent by a length-5 sequence of ones, i.e., 1 → (1,1,1,1,1). Assume that information bits "O's" and "1's" are sent with equal prob- ability and each of the 5 corresponding code bits that are transmitted are received in error independently with probability 0.01. The receiver makes a...
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 communication system that transmits information using the pulse g(t) = A[−u(t) + 2u(t...
Consider a binary communication system that transmits information using the pulse g(t) = A[−u(t) + 2u(t − T /2) − u(t − T )] according to the mapping rule “0′′ → −g(t) “1′′ → +g(t) The “0”s and “1”s are transmitted with equal probability, and the channel is an AWGN channel, with a two-sided noise power spectral density of No/2 watts/Hz. a) Determine and sketch the filter h(t) that is matched to g(t). b) Determine and sketch the overall pulse...
8. There are three urns. Urnl contains 2 white and 3 black marbles, Urn2 contains 3...
8. There are three urns. Urnl contains 2 white and 3 black marbles, Urn2 contains 3 white and 2 black marbles, and Urn3 contains 1 white and 4 black marbles. First, the urn is selected equally likely, than a ball is drawn from the urn. a) We know that a white marble is chosen. What is the probability that the marble came from Urn2? b) We know that a black marble is chosen. What is the probability that the marble...
4{ 73%. 12:46 PM hw2 - Read-only Read Only - You can't save changes to this...
4{ 73%. 12:46 PM hw2 - Read-only Read Only - You can't save changes to this file ECE 3U2 Homework z Due date: January 24, 2019 (Thursday), before clas:s 1. (10 points) A lot of 100 items contains k defective items. M (Ms100) items are chosen at random and tested (a) (2 pts) How many different ways can we choose M items from 100 items in the lot? (b) (4 pts) How many different ways that among the M items...
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)
2. Consider a binary communication channel The probability that a transmitted 0 is received as 1 is ε1- The probability that a transmitted 1 is received as 0 is Assume that the 2 transmitted inputs have equal probabilities. a) (10 points) Find the probability that the output received is 0. b) (10 points) Find the probability that the transmitted input is 0 given that the received output is 1 e) (5 points) Find the probability that the transmitted input is...
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...
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....
A communication link uses a simple repetition code for error correction, where ain information bit T)" is sent by a length-5 sequence of zeros, İ.е., 0 (0,0,0,0,0) Likewise, an information bit "I', is sent by a length-5 sequence of ones, i.e., 1 → (1,1,1,1,1). Assume that information bits "O's" and "1's" are sent with equal prob- ability and each of the 5 corresponding code bits that are transmitted are received in error independently with probability 0.01. The receiver makes a...
8. There are three urns. Urnl contains 2 white and 3 black marbles, Urn2 contains 3 white and 2 black marbles, and Urn3 contains 1 white and 4 black marbles. First, the urn is selected equally likely, than a ball is drawn from the urn. a) We know that a white marble is chosen. What is the probability that the marble came from Urn2? b) We know that a black marble is chosen. What is the probability that the marble...
4{ 73%. 12:46 PM hw2 - Read-only Read Only - You can't save changes to this file ECE 3U2 Homework z Due date: January 24, 2019 (Thursday), before clas:s 1. (10 points) A lot of 100 items contains k defective items. M (Ms100) items are chosen at random and tested (a) (2 pts) How many different ways can we choose M items from 100 items in the lot? (b) (4 pts) How many different ways that among the M items...
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