$M{l}_4$

Rant I: A source produces binary characters $\{0,1\}$ in an Independent & Irantially Distidented tisi fastuin accurding to the probability: & $(1)=0\mathrm{.}8$

A symbol$-$by$-$Symbel data compestar is firist considued. By how mucl can you compress?

Explain

Throng incatenating, design a cmplession scheme that compuses by at least $20\%.$

Make sure to Aferify your design and quantify its per formance.

Part II: Now conside The since on $S=\{a$;$b$;$c\}$ IID Yo not that "labeling" the edges of a "tuffman "then" is dore abitharily so

$e$:$a1,e^{\text{'}},$alongrightarrow$0$

$b01\frac{?}{?}$& $b11$

$c11,$clongrightarrow$10$

one both oftimal. We world like to compuess the ontput of $e($a $e^{\text{'}})$

$3]$ With this in mind, are $e$&$e^{\text{'}}$ equivalent? i$.$e$.$ are They botte as grod$/$bod$?$ Elabrate $4)$ Lipose a metrod $($NOT BASED ON CONCATENAIION$)$ to improve The ontfut.