Question: 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

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. We start out with a symmetric binary communication channel characterized by the conditional probabilities Pr[0R|0S] = Pr[1R|1S] = 0.975 and Pr[0R|1S] = Pr[1R|0S ] = 0.025. The prior probabilities of a 0 or a 1 are given by Pr[0S ] = 0.512 and Pr[1S ] = 0.488. The input to the binary communication channel is to be a sequence of 0s and 1s. Each 0 or 1 in the sequence is statistically independent of the others and is generated according to the probabilities Pr[0S ] and Pr[1S ] given above. 1. Generate the data input sequence of 0s and 1s according to the required prob- abilities. The size of the sequence is your choice; however, to obtain meaningful results, it should be at least 5000 points long. 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 gen- erate an output of 0 with probability Pr[0R|0S] and an output of 1 with probability Pr[1R|0S ] (where these numerical values are given above). (b) When a 1 is presented to the channel, the channel should generate a 0 with probability Pr[0R|1S ] and a 1 with probability Pr[1R|1S]. 3. Compute the theoretical values for the following probabilities: Pr[0S|0R], Pr[1S|1R], and Pr[error] (see Section 2.5.1). 4. Apply the input data sequence generated in Step 1 to the channel in Step 2, estimate the probabilities in Step 3. To estimate the probability, use relative frequency; for example, to estimate Pr[0S|0R] you would compute # times 0 sent and 0 received # times 0 received 5. Compare the estimated values to the theoretical values. If necessary, repeat the experiment using a longer input sequence. You may also wish to compare the results for various length input sequences. Repeat Steps 1 through 5 for a nonsymmetric binary communication channel with conditional probabilities Pr[0R|0S] = 0.975, Pr[1R|1S ] = 0.9579, Pr[1R|0S ] = 0.025, Pr[0R|1S ] = 0.0421. Let the prior probabilities be Pr[0S] = 0.5213 and Pr[1S] = 0.4787. MATLAB programming notes You can generate a binary random number with the following statement: x=rand(1)

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