$($c$)$ Consider $64$QAM constellation with minimum distance $d_{\text{m}\text{i}\text{n}}=2$ :

$($i$)$ How many bits for either I or Q channel? Write down pairs of bits for either I

or Q channel with Gray coding.

$($ii$)$ Let $b_3{b}_2{b}_1$ denote three bits relatively, do $b_1,$ and $b_2$ have the same immunity

to noise? What are the decision rules for each bit?

$($iii$)$ What is the average Bit Error Rate $($BER$)$ given noise power is ${}^2=0\mathrm{.}5?$