Consider the encoding $C$:$x{D}^{**}$ where $D=\{a,b\}$ and

$Cl,\{\begin{array}{cc}\text{:}[x,& D^{**}]\\ & \text{b}\text{a}\text{b}\text{a}& \\ & \text{a}\text{b}\text{b}\text{a}& \\ & ab\\ & bbb\\ & aa\\ & \text{a}\text{b}\text{b}& \end{array}$

$2+4+3+5+1=15$

$($a$)$ Is $C$ a prefix code? Justify.

$($b$)$ If $C$ is not a prefix code, is it uniquely decodable? Justify.

$($c$)$ If $C$ is uniquely decodable, give an algorithm to decode.

$($d$)$ If $C$ is uniquely decodable, how much look$-$ahead does your decoder need? Can you manage with finite look$-$ahead?

$($e$)$ Is $C$ an instantaneous code? If yes, give an algorithm. If no$,$ justify.