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Ch. 8 Multiplexing

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**Ch. 8 Multiplexing 8.1 Frequency-Division Multiplexing**

8.2 Synchronous Time-Division Multiplexing 8.3 Statistical Time-Division Multiplexing 8.4 Asymmetric Digital Subscriber Line 8.5 xDSL

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**8.1 Frequency-Division Multiplexing**

FDM--Definition The division of a transmission facility into two or more channels by splitting the frequency band transmitted by the facility into narrower bands, each of which is used to constitute a distinct channel.

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**8.1 Frequency Division Multiplexing (p.2)**

FDM-- Figure 8.4 Incoming signals are each modulated using a different carrier frequency (N sources.) The channels are separated by guard bands, which are unused portions of the spectrum. The spectrum of the composite signal is shown in Figure 8.4b. The receiver consists of bandpass filters and demodulators, centered around each carrier frequency.

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**8.1Frequency Division Multiplexing (p.3)**

Examples of FDM Example 8.1 Broadcast and cable TV Three source signals: black-and white video, color information, and audio. All three fit in a 6 M Hz bandwidth. Each of these can be treated as 1 channel (Table 8-1) and multiplexed together. Example 8.2 Voiceband Signals 4 k Hz bandwidth (effective bandwidth 300 to 3400 Hz). SSBSC--single sideband, suppressed carrier. Use 64k Hz, 68k Hz, and 72k Hz carriers (Fig. 8-5).

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**8.1 Frequency Division Multiplexing (p.4)**

Analog Carrier Systems (Table 8.1) FDM --earliest carrier system and still is common. AT&T (North American Standard) Group--12 voice channels Supergroup--5 groups (60 voice channels) Mastergroup-10 supergroups (600 voice channels)

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**8.1 Frequency Division Multiplexing (p.5)**

Wavelength Division Multiplexing Multiple beams of light are transmitted at different frequencies on the same fiber. 1997--Bell Labs demonstrated 100 beams each operating at 10 G bps, for a total data rate of 1 trillion bits per second (1 terabit per sec). Commercial systems with 160 and 256 channels are currently available.

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**8.1 Frequency Division Multiplexing (p.6)**

Problems with FDM carrier systems: Crosstalk and intermodulation noise. Must demodulate all signals for switching. Inflexible.

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**8.2 Time-Division Multiplexing**

TDM--Definition The division of a transmission facility into two or more channels by allotting the facility to several different information channels, one at a time.

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**8.2 Time-Division Multiplexing(p.2)**

STDM--Definition A method of TDM in which time slots on a shared transmission line are assigned to I/O channels on a fixed, predetermined basis. Each channel could carry a bit, byte, or block, depending on implementation. In general, start and stop bits are stripped off, if asynchronous terminals are being multiplexed. See Fig. 8.6.

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**8.2 Time Division Multiplexing (p.3)**

STDM Link Control Blocks of bits are the input sources (eg. HDLC). Flow control, error control, etc. will be handled before and after the multiplexers. Framing There is some framing required. Added-digit framing--a single bit is added to each frame; the bits will form a repetitive pattern.

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**8.2 Time Division Multiplexing (p.4)**

Pulse Stuffing Suppose that the outgoing data rate of the multiplexer, excluding framing bits, is higher than the sum of the maximum instantaneous incoming rates. Excess capacity is used by stuffing extra dummy bits or “pulses” into each incoming signal until its rate is raised to that of a locally-generated clock signal. Solves problems of synchronization among data sources.

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**8.2 Time Division Multiplexing (p.5)**

Example STDM-- (Fig.8.8) Digital and Analog Sources Source 1 Analog 2 kHz bandwidth (16 kbps). Source 2 Analog 4 kHz bandwidth (32 kbps). Source 3 Analog Sources 4-11: Digital Each of the eight sources is a 7200 bps synchronous data stream.

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**8.2 Time Division Multiplexing (p.6)**

Example STDM-- (Fig.8.8) (cont.) Analog sources Sampled and encoded using 4 bits. Gathered into one 16-bit buffer . Result is a 64 k bps multiplexed information stream. Resulting analog source frame is Source 1 (4 bits), Source 2 (4 bits), Source 3 (4 bits), Source 2 (4 bits). Digital sources Each is increased to 8 k bps using pulse stuffing. TDM signal: 64 k bps + 8 x 8 k bps =128 k bps. Extra Study Question: What would a frame look like?

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**8.2 Time Division Multiplexing (p.7)**

Digital Carrier Systems Standards North American and ITU-T are different. Table 8.3 (DS-1 through DS-4; Levels 1-5)

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**8.2 Time Division Multiplexing (p.8)**

DS-1 Transmission Format (Fig. 8-9) Frame Structure (193 bits) 8 bits/channel 24 channels 1 framing bit. Data Rate 193 bits/frame x 8 k frames/sec =1.544 Mbps.

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**8.2 Time Division Multiplexing (p.9)**

DS-1 Transmission Format (Fig. 8-9)(cont.) Voice Uses bit robbing. Every sixth frame has one bit "robbed" for control signaling from each channel. Data Bit 8 is used for control signaling (8,000 bps.) Bit 1-7 used for 56 kbps service. Bit 2-7 used for 9.6, 4.8, and 2.4 kbps service.

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**8.2 Time Division Multiplexing (p.10)**

SONET/SDH An optical transmission interface. Signal Hierarchy--Table 8.4. Frame Formats--Fig.8.10 and 8.11.

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**8.3 Statistical TDM Statistical TDM--Definition**

A method of TDM in which time slots on a shared transmission line are allocated to I/O channels on demand (dynamically.) Also known as asynchronous TDM.

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8.3 Statistical TDM (p.2) More efficient than synchronous TDM in some cases, since some synchronous TDM slots go unused. Synchronous TDM is more like "reserved seating" and Statistical TDM is "open seating". Definition: The "aggregate" data rate is the nominal data rate of all the sources combined; it is generally larger than the actually data rate on the multiplexed line.

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**Architecture 8.3 Statistical TDM (p.3)**

Each I/O line has a buffer (eg, UARTs.) The buffers are scanned for new characters. Address information is added and the result is placed in an outgoing block (ie, a FIFO queue). Two multiplexors could exchange blocks using a data link protocol such as HDLC. See Fig and 8.13.

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**8.3 Statistical TDM (p.4) Performance**

Problem: Peak load may exceed the transmission line data rate between the MUX’s. Solution: Buffer is used to hold incoming characters from terminals. Example: Table 8-6 Input: number of bits from the sources in 1 msec. Output: number of bits transmitted in 1 msec. Backlog: length of buffer--bits that have to wait. Increasing the transmission data rate reduces the backlog.

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**Performance Model Example**

8.3 Statistical TDM (p.5) Performance Model Example I = number of input sources= 10. R= data rate of each source = 1,000 bps. IR= aggregate data rate = 10, 000 bps. M=outgoing transmission line rate (in bps.) case 1: 5000 bps case 2: 7000 bps K= M/(IR) case 1: 5000/10,000 = .5 case 2: 7000/10,000 = .7 a= amount of time each source is active = .5

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**Single Server Queue Performance Model**

8.3 Statistical TDM (p.6) Single Server Queue Performance Model What is the delay through the queue? What is the average length of the queue? What is the probability of overflow? Assumptions for Statistical TDM: Random (Poisson) arrivals. Constant "service" time. FIFO Queue . Table 8.7 Formulas for Single-Server Queue.

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**8.3 Statistical TDM (p.7) Queue Parameters Formulas**

l= arrival rate of "messages" (per second). Ts= mean service time for each arrival (secs/message). r= fraction of time facility is busy (utilization.) N= no. of messages in system (buffer size). Tr= average time a message is in the system (delay). Formulas See Table 8.7

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**Statistical TDM as a Queue:**

8.3 Statistical TDM (p.8) Statistical TDM as a Queue: Arrival rate into the queuing system: l= a IR = .5 x 10,000 bps = 5,000 bps. Service time of each arrival: Ts = 1/M Utilization r = l Ts = a I R/M = a/K = l/M case 1: r1 = 5,000 bps/5,000 bps = 1 case 2: r2 = 5,000 bps/7,000 bps = .71

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**As r increases, delay increases.**

8.3 Statistical TDM (p.8) Performance Curves Fig. 8.14a.Buffer Size vs. Utilization As r increases, the average number of messages waiting in the queue increases. Fig. 8.1b. Mean Delay vs. Utilization Three curves for different M’s. As M increases, delay decreases (fixed r). As r increases, delay increases.

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**Performance Curves (cont.)**

8.3 Statistical TDM (p.9) Performance Curves (cont.) Fig Probability of Overflow vs. Max Buffer Size Probability of overflow decreases with an increase in Max Buffer Size ( for a fixed r). Decreasing r will decrease the probability of overflow.

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**Which one has a reasonable delay? **

8.3 Statistical TDM (p.10) Recall Example case 1: r1 =1 case 2: r2 =.71 Which one has a reasonable delay? Which one has a reasonable average buffer size? Which one has a reasonable maximum buffer size?

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**8.3 Statistical TDM (p.11) Cable Modem**

Two channels--one in each direction. Channels are shared--type of statistical multiplexing.

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**8.4 Asymmetric Digital Subscriber Line**

ADSL Design (Fig. 8.17) ADSL provides more capacity down-stream than upstream. Although originally conceived for video-on-demand, it is being used for Internet access. Lowest 25kHz are reserved for voice (POTS) Separate Upstream and Downstream (FDM). Overlapping Upstream and Downstream (FDM with echo cancellation.) Discrete Multitone Transmission (DMT) is used.

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8.5 xDSL ADSL is one of several schemes for high-speed transmission on a subscriber line. Other schemes are summarized in Table 8.8 High Data Rate Digital Subscriber Line Single Line Digital Subscriber Line Very High Data Rate Digital Subscriber Line

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