1. Theory: Question B & C
For this task it has ask me to construct the ML(Maximum Likelihood) Table.
Finally, I need to find the probability that the ML(Maximum Likelihood) decoding fails to make a correct decision when the C(codeword) is transmitted.

2. Working out: part 1
To do the ML(Maximum likelihood) table the first I thing I did was use the:
generator Matrix:
Draw an 8th bit table:
Convolution Code
Transpose

3. Working out: part 2 This is the complete table.
As you can see from the table C4: is the codeword as it match our theory question codeword
Convolution Code
Transpose the Genrator Matrix afterward you times with B and you get the answer

4. Working out: Part 3
For this part we need draw out the ML (Maximum Likelihood) table for this we need
Draw a 32 bit table:
Have c1 – c7 sub-heading
Wrong and Correct (W/C)
Probability

5. Working out: Part 4 For this part we will need to workout: c1-c7
Decision
Wrong Correct (W/C)
Probability
In the next slides I explain how we will work out this problems.

6. Working out: Solution to c1-c7 and decision
To work out you will need the 32 bit
Add the codeword number (c1-c7) with The error bit
Calculate how many one you have left and you it in
the table
Decision:
To work out the decision you look at c1-c7 what the smallest answer you got you put in the number for example:

7. Working out: Solution to Wrong Correct (W/C) and probability
Basically you look at the decision table it the answer is not C4 then you put a 1 but if the answer is a C4 then you put a 0
- 1 means error
- 0 means no error
Probability:
– Codeword Given = 0 (1-pb)
– First bit = 1 (pb)
– Answer
pb^3 x (1-pb)^2
Also if your (W/C) is zero you put no error also if you had a half in (W/C) you also need to put a half at the end of your answer.
C4 being the codeword
^ power of

8. Complete Maximum likelihood decoding
As you can Number 7 and number 15 as they both contain 0 are the only correct decision when the C(codeword) is transmitted.