Digital modulations and coding techniques are the building blocks of

wireless communication systems.

$($a$)$ Briefly explain the different types of HARQ process. Which type of

HARQ process is implemented in the Physical layer of the LTE

system?

$(5$ marks$)$

$($b$)$ Consider the use of Hamming codes to send $11-$bit messages.

Specifically, consider the message $10011011011.$ First, calculate the

Hamming codeword for this message. Second, invert one message bit

in that Hamming codeword $($to represent a $1-$bit error$)$ and show how

the recipient can use the check bits to correct the inverted bit. $($That is$,$

perform the error correction.$)$

$(5$ marks$)$

$($c$)$ Draw a block diagram of the QAM modulator. Explain how does a

QAM system conserve bandwidth.

$(5$ marks$)$

$($d$)$ 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$1=111011$

Notation is follows: if the generator polynomial is$,$ say, $1101,$ then the

corresponding parity bit for message bit n is $($x$[$n$]+$ x$[$n$-1]+$ x$[$n$-3])$ mod

$2$ where x$[$n$]$ is the message sequence.

$$ Find the code rate and constraint length of the two

schemes. $(1$ mark$)$

$$ How many states will there be in the state diagram for

Scheme I and Scheme II$?(2$ marks$)$

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