A source delivers bits to be transmitted at the rate $56000$ per second. The white noise power has spectral density level $108$ W$/$Hz$.$ The transmitted signal power is $1$ kW$,$ and the path loss is $60$dB$.$ The modulation used is DPSK$.$ A Hamming $(7,4)$ code is being considered. $($a$)$ What are the times per bit, with coding and without? $($b$)$ What are the probabilities of a channel bit error $($that is$,$ prior to decoding, in the Hamming code case$)$ with and without coding? $($c$)$ What is the probability of a channel word error if coding is used? $($d$)$ Is it better to code or not to code?