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Chapter 4

Digital Transmission

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4-1 4-1 DIGITAL-TO-DIGITALDIGITAL-TO-DIGITAL CONVERSIONCONVERSION

In this section, we see how we can represent digital In this section, we see how we can represent digital

data by using digital signals. The conversion involves data by using digital signals. The conversion involves

three three techniques:techniques: lineline codingcoding,, blockblock codingcoding,, andand

scrambling scrambling.. LineLine codingcoding isis alwaysalways needed;needed; blockblock

coding and scrambling may or may not be needed. coding and scrambling may or may not be needed.

 Line Coding

 Line Coding Schemes

 Block Coding

 Scrambling

Topics discussed in this section: Topics discussed in this section:

Figure 4.1 Line coding and decoding

Mapping Data symbols

onto Signal levels

 A data symbol (or element) can consist of a number of data bits:  (^1) , 0 or  (^) 11, 10, 01, ……  A data symbol can be coded into a single signal element or multiple signal elements  (^1) -> +V, 0 -> -V  (^1) -> +V and -V, 0 -> -V and +V  The ratio ‘r’ is the number of data elements carried by a signal element.

Figure 4.2 Signal element versus data element

Data rate and Baud

rate

 The baud or signal rate can be expressed as: S = c x N x 1/r bauds where N is data rate c is the case factor (worst, best & avg.) r is the ratio between data element & signal element

Although the actual bandwidth of a

digital signal is infinite, the effective

bandwidth is finite.

Note

The maximum data rate of a channel (see Chapter 3) is

Nmax = 2 × B × log

2

L (defined by the Nyquist formula).

Does this agree with the previous formula for N

max

Solution

A signal with L levels actually can

carry log 2 L bits per level. If each

level corresponds to one signal element

and we assume the average case (c =

1/2), then we have

Example 4.

Line encoding C/Cs

 DC components - when the voltage level remains constant for long periods of time, there is an increase in the low frequencies of the signal. Most channels are bandpass and may not support the low frequencies.  This will require the removal of the dc component of a transmitted signal.

Line encoding C/Cs



Self synchronization - the

clocks at the sender and the

receiver must have the same

bit interval.



If the receiver clock is

faster or slower it will

misinterpret the incoming bit

stream.

In a digital transmission, the receiver clock is 0.1 percent

faster than the sender clock. How many extra bits per

second does the receiver receive if the data rate is

1 kbps? How many if the data rate is 1 Mbps?

Solution

At 1 kbps, the receiver receives 1001

bps instead of 1000 bps.

Example 4.

At 1 Mbps, the receiver receives 1,001,000 bps instead of

1,000,000 bps.

Line encoding C/Cs

 Error detection - errors occur during transmission due to line impairments.  Some codes are constructed such that when an error occurs it can be detected. For example: a particular signal transition is not part of the code. When it occurs, the receiver will know that a symbol error has occurred.

Line encoding C/Cs



Complexity - the more robust

and resilient the code, the

more complex it is to

implement and the price is

often paid in baud rate or

required bandwidth.

Figure 4.4 Line coding schemes