$($d$)$ A time division multiple access $($TDMA$)$ system operates at $20Mbps$ with a frame length of $1ms.$ Assume that all the time slots are of equal duration and require a preamble of $100$ bits in addition to a time guard band of $1s.$

$($i$)$ Determine the maximum number of equal data$-$rate users that can be multiplexed if the system efficiency must be kept at $95\%$ or above.

$($ii$)$ Can this system accommodate $100$ equal data$-$rate users? Show your calculations to justify your answer.

$($iii$)$ If the minimum data rate per user is to be maintained at no less than $1$ Mbps$,$ what is the maximum number of users that can be multiplexed and what would be the exact bit rate per user?

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