Consider a communications channel being used by a cable modem network. The channel has use of the spectrum between $204MHz$ and $220MHz.$ The signal power is $30mW$ and the noise power is $3mW.$

a$.$ Interpret the theoretical maximum capacity of the channel in bps$.$

b$.$ Assuming the capacity of the channel using half of its data rate, determine how many signal levels would be needed?

c$.$ If we change the bandwidth to $10MHz.$ How changes in signal levels should be made to maintain the same data rate?