A pseudo-random signal (S) of -3 or 3 is transmitted over a noisy channel. S=-3 is transmitted with probability of 1/3. The received signal, Y, is the sum of the sent signal and the noise, N. The noise is modeled as a normal Gaussian with E[N]=0,var(N)=4 . The received signal is decoded as -3 for Y≤−0.5 and 3 for Y>−0.5. a. What is the probability of error in this

A pseudo-random signal (S) of -3 or 3 is transmitted over a noisy channel. S=-3 is transmitted with probability of 1/3. The received signal, Y, is the sum of the sent signal and the noise, N. The noise is modeled as a normal Gaussian with E[N]=0,var(N)=4 . The received signal is decoded as -3 for Y≤−0.5 and 3 for Y>−0.5. a. What is the probability of error in this

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Question

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A pseudo-random signal (S) of -3 or 3 is transmitted over a noisy channel. S=-3 is transmitted with probability of 1/3. The received signal, Y, is the sum of the sent signal and the noise, N. The noise is modeled as a normal Gaussian with E[N]=0,var(N)=4 . The received signal is decoded as -3 for Y≤−0.5 and 3 for Y>−0.5.

a. What is the probability of error in this system?

b. To improve the system, each signal is transmitted three times and output is determine by majority rule (2 or more). What is the new probability of error?

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