Consider that a $100-$kbits$/$s data stream is to be transmitted on a voice$-$grade telephone circuit $($with a bandwidth of $3$ kHz $).$ Is it possible to approach error$-$free transmission with an SNR of $10$ dB $?$ Justify your answer. If it is not possible, suggest system modifications that might be made. $[20$ POINTS$]$

Consider a telephone modem operating at $28\mathrm{.}8$ kbits that uses trellis$-$coded QAM modulation. $[20$ POINTS$]$

a$.$ Calculate the bandwidth efficiency of such a modem, assuming that the usable channel bandwidth is $3429$ Hz $.$

b$.$ Assuming AWGN and an available $E$

$u{N}_0=10dB,$ calculate the theoretically available capacity in the $3429$ Hz bandwidth.

c$.$ What is the required $E_b{N}_0$ that will enable a $3429$ Hz bandwidth to have a capacity of $28\mathrm{.}8$ kbits s$?$