Project 1
In a binary communication system, the probability of transmitting a “1” and “0” are 0.3 and 0.7, respectively. Relays (i.e., repeaters) are needed for long distance transmissions. (Each repeater takes the output from the previous one as input.) Suppose that each transmission-reception has an error rate of p1=0.1.
(a) Predict the probability of getting a “0” after many repeats (say 60) before your simulation. Give your reason(s). You can use equations if you wish.
(b) Simulate the repeaters by generating an error probability of 0.1 for each relay. Propagate the results through the relays. Plot the probability of getting a 0 as a function of number of relays, nr, for nr=1:60. Does the result agree with your prediction? Why? (You need to have a random number generator in order to get an error of 0.1. Here you do 1 million random experiments to see what the results are. Here you do not even need to know the total probability theorem.)
(c) If a “0” is transmitted, what is the requirement on the error rate for each transmission-reception such that we have a 95% probability of correctly receiving it after 20 repeats? Estimate this error rate with approximations.
(d) Model the result in (c) by applying the theoretical calculation for each relay. Propagate the result through each relay. If there is a discrepancy between your calculation in (c) and the modeling result, discuss the reason(s) for such a discrepancy. (In modeling, you use a computer to obtain results based on a theoretical model that cannot be solved easily by hand. You can use total probability theorem here.)
(e) If a sequence of 16 bits is transmitted and received with a bit error of 0.1, what is the probability that at least one bit is wrong (assuming P(transmitting 0)=0.7))? If the last bit is a parity bit, what is the probability of knowing a transmission error has occurred? You can read the description of the parity bit at https://en.wikipedia.org/wiki/Parity_bit. Does it matter if even or odd parity is used here?
Report Requirement
In your project report, you need to
Describe the process of getting the answers and explain your graph or table. You have to make it understandable to students with basic knowledge of the pre-requisites and the course materials covered so far. In general, you should type it up in a word document and copy and paste any relevant results from Matlab.
Append your matlab programs at the end of your document or submit them as separate files.
Organize your report according to the questions asked.
Submitting only matlab files will result in very few points.