$($a$)$ Consider two convolutional coding schemes $-$ I and II$.$ The generator

polynomials for the two schemes are

Scheme I: G$0=1101,$ G$1=1110$

Scheme II: G$0=110101,$ G$1=111011$

$($i$)$ What are the code rates $($r$)$ and constraint lengths $($k$)$ for the two

schemes?

$($ii$)$ How many states will there be in the state diagram for Scheme I?

For Scheme II$?$

$($iii$)$ Which code will lead to a lower bit error rate? Why?

$($iv$)$ Alyssa P$.$ Hacker suggests a modification to Scheme I which

involves adding a third generator polynomial G$2=1001.$ What is

the code rate r of Alyssa's coding scheme? What about constraint

length k$?$ Alyssa claims that her scheme is stronger than Scheme I.

Based on your computations for r and k$,$ is her statement true?