1. Maximum Likelihood Detection
Dr. Muqaibel

4. Example
A binary repetition code is used where 0 is encoded as 000 and 1 is encoded as 111. What is your decoding decision if what you receive over a BSC with cross over probability=0.3 is 101.
Using Minimum Distance Decoding.
Using Maximum Likelihood detection if p(0)=0.8 & p(1)=0.2.
Comment

5. Matlab illustration % Dr. Ali Muqaibel 072 March 2008
%c1:000 c2=111 r=101
pc1=0:0.01:1;
pc2=1-pc1;
t2=1;
t1=2;
p=0.3;
y=t1-t2-log(pc2./pc1)/log(p/(1-p)); % note log(p/(1-p)) is a negative number which flips the probability.
plot (pc1,y)
xlabel ('pc1')