I would like to understand how to obtain a Gray coding of bits onto the signal points of 8-PSK.
According to the Matlab website, one example is
I understand that in Gray coding, the neighboring points can only differ by 1 bit. Also, the allocation in the example above is worked out using phasors in the output. But is this set of Gray codes fixed? If not, how do I determine which signal point is mapped to which Gray code? Is it arbitrary? For example, instead of assigning the point on the positive horizontal axis "000", then work out the other points from there, can I assign "111" to that point, then work out the other Gray codes from there?
Do I get another set of Gray codes if I rotate the code assignment, say, by 45 degrees? Is the below still a valid set of Gray coding?
What about the example below?
