Question 4: A binary communication system transmits signals through an Additive White Gaussian Noise (AWGN) channel. The system can select between uncoded and code modes. In coded mode, channel coding using a linear block code is used. The generator matrix of the code is given as: 100 G = Assuming the Gaussian noise w has following probability density function (pdf): S(w) a) Construct the Maximum Likelihood decoding rule for the coded case b) Find the error probability when the specific codeword of c =[1110] is transmitted

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Question 4:
A binary communication system transmits signals through an Additive White Gaussian Noise
(AWGN) channel. The system can select between uncoded and code modes. In coded mode,
channel coding using a linear block code is used. The generator matrix of the code is given as:
1 0 0 1
G =
0 1
1
Assuming the Gaussian noise w has folowing probability density function (pdf):
f(w) =
a) Construct the Maximum Likelihood decoding rule for the coded case
b) Find the error probability when the specific codeword of e = [1110] is transmitted
c) Find the new error probability in question (2.b) when the Gaussian noise is replaced by a
Laplacian noise with the following pdf:
f(w) =
Transcribed Image Text:Question 4: A binary communication system transmits signals through an Additive White Gaussian Noise (AWGN) channel. The system can select between uncoded and code modes. In coded mode, channel coding using a linear block code is used. The generator matrix of the code is given as: 1 0 0 1 G = 0 1 1 Assuming the Gaussian noise w has folowing probability density function (pdf): f(w) = a) Construct the Maximum Likelihood decoding rule for the coded case b) Find the error probability when the specific codeword of e = [1110] is transmitted c) Find the new error probability in question (2.b) when the Gaussian noise is replaced by a Laplacian noise with the following pdf: f(w) =
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