The modulation scheme used for Digital Subscriber Lines is called $$Discrete MultiTone $($DMT$).$ The way it works is that the available spectrum of the DSL phone line is partitioned into $2504-$KHz sub$-$channels $($just like Frequency$-$Division Multiplexing for different user channels$),$ some of which are allocated for upstream $($home to central office $($CO$)),$ the rest for downstream $($CO to home$)$ data transmissions. Suppose that there is no excess bandwidth, so that the symbol rate in each sub$-$channel is fixed at $4000$ symbols per second. Suppose $32$ of these channels are allocated for the upstream. For a given user, signal$-$to$-$noise ratio measurements on these channels indicate that $2$ of these channels can support $256-$QAM, $4$ of them can afford $64-$QAM, $6$ of them can use $16-$QAM, and $8$ of them must use $4-$QAM, and the remaining $12$ channels are too noisy to transport data. Based on DMT modulation, user data are transmitted over these $32$ channels in parallel so that the user data rate equals the sum of the data rates over all of these channels. Find the upstream data rate for this use