In a binary communication system, the probability of transmitting a 1 and 0 are 0.4 and 0.6, respectively. Relays are needed for long distance transmissions. Suppose that each transmission-reception has an error rate of p1=0.1.

(a) Predict the probability of getting a "0" after many relays (say 60) before your simulation.

(b) Plot the probability of getting a 0 as a function of number of relays, nr, for nr=1:40. Does the result agree with your prediction? Why?

(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 relays? Justify your error rate with calculations.

(d) Run a simulation to verify your result, if there is a discrepancy between your calculation and the simulation, discuss the reason(s) for such a discrepancy.

Report Requirement

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.

USE MATLAB!