Problem $3$

A source generates one frame of $200$ data bits every $10mS.$ Each frame is added $20CRC$ bits, and then

passed through the $(15,11)$ Hamming encoder, as simulated in Problem $2.$ The coded data then goes into

an interleaver that operates on a frame$-$by$-$frame basis $($its depth is one frame$),$ and a PSK modulator

with raised$-$cosine pulse shaping. The receiver channel decoder is based on Syndrome decoding, and the

range of the radio link is $4km$ at a BER of $2{10}^{-4}.$

$($a$)$ Find the number of Hamming blocks that fit into one frame, and the depth of the interleaver in bits.

$($b$)$ Knowing that the radio channel has an available bandwidth of $40kHz,$ find the maximum value of

roll$-$off factor that can be used.

$($c$)$ Suppose that we want to extend the range of the radio link to $5km.$ Would switching from Syndrome

decoding to soft decoding at the receiver $($leaving all other system parameters unchanged$)$ be enough to

support this upgrade and still maintain the same BER? Assume that the radio signal attenuates as a

function of $d^2.$

$($d$)$ What would be the engineering cost of implementing the upgrade described in $($c$)?$