We want to study the basic ISDN $($Integrated Service Digital Network$)$ interface, which allows three channels to pass simultaneously on the same link. This interface, marketed by many operators, allows two telephone channels and one data channel to pass through. The two telephone channels offer a speed of $64$ Kbit$/$s$,$ and the data channel a speed of $16$ Kbit$/$s$.$ The interface being digital, a telephone communication can be directly replaced by a data transfer at a speed of $64$ Kbit$/$s$.$

a$)$ The multiplexing being temporal, and the overall frame containing all of the three slices associated with the three simultaneous communications lasting $125$s$,$ deduce the structure of this frame.

b$)$ Knowing that, in the frame, $6$ bits must be added for signaling and synchronization, what is the overall speed of the basic ISDN interface?

c$)$ The primary ISDN interface allows, under similar conditions, to pass thirty telephone channels at $64$ Kbit$/$s and one data channel at $64$ Kbit$/$s over a physical link. What should be the structure and flow rate of the high$-$speed channel if time multiplexing is carried out with a frame duration always equal to $125$s$?$

d$)$ In fact, there is an additional channel with a speed of $64$ Kbps for signaling and synchronization. What is the overall speed of the interface? Why was this speed chosen?

e$)$ Unlike the Europeans, the Americans chose a primary interface of twenty$-$three telephone channels and a signaling and synchronization channel. All these channels having a throughput of $64$ Kbit$/$s$,$ what is the overall capacity of the interface? Why such a difference with what is happening in Europe?

f$)$ Is it possible to consider statistical multiplexing on the primary interfaces?

g$)$ What is the benefit for a user of subscribing to the basic ISDN interface rather than subscribing to two telephone lines?

h$)$ We now want to compare network access via an ADSL modem on a telephone line and access via a cable operator. Are multiplexing techniques comparable? Compare them to the multiplexing technique used in the RN$.$