Chapter 4
DIGITAL-TO-DIGITAL CONVERSION
Objective
❑ The first section discusses digital-to-digital conversion.
❑ Line coding is used to convert digital data to a digital signal.
4-1 DIGITAL-TO-DIGITAL CONVERSION
•Discuss how to represent digital data by using digital signals.
•The conversion involves three techniques:
1.Line coding, 2.Block coding 3.Scrambling.
•Line coding is always needed; block coding and scrambling may or may not be needed.
Line Coding
•Line coding is the process of converting digital data to digital signals.
•We assume that data in the form of text, numbers, graphical images, audio, or video, are stored in computer memory as sequences of bits.
• Line coding converts a sequence of bits to a digital signal.
•At the sender, digital data are encoded into a digital signal;
•At the receiver, the digital data are recreated by decoding the digital signal.
Line coding and decoding
Common characteristics
1. Signal element versus Data element
■ In Data Communication, goal is to send data elements.
A Data element is a smallest entity that can represent a piece of information – a bit.
■ Signal element carries the data elements.
A Signal element is the shortest unit(time wise) of a digital signal.
i.e data elements are what we need to send(Being carried), Signal elements are how we can send(carriers).
Define a ratio r which is the number of data elements carried by each signal element.
Signal elements versus data elements
Continued..
1. One data element is carried by one signal element(r=1)
2. Two signal elements(2 transitions) to carry each data element(r=1/2)
3. A signal element carries 2 data elements(r=2)
4. A group of 4 bits being carried by a group of three signal elements(r=4/3).
Data rate VS Signal rate
■ Data rate(N) (bit rate) Number of data elements(bits) sent in 1s.
■ Unit is bps.
■ Signal rate(S)(Pulse rate) Number of signal elements sent in 1s.
■ S=N/r Unit is baud.
■ Relationship between data rate and signal rate depends on value of r(No. of DE carried by SE) & on the bit pattern.
■ Defines three cases: worst, best & Average. Worst case is when we need maximum signal rate, best is when we need minimum .
■ In Data Communication, Average case relationship b/w data rate
& signal rate is , measured in baud
A signal is carrying data in which one data element is encoded as one signal element (r = 1). If the bit rate is 100 kbps, what is the average value of the baud rate if c is between 0 and 1?
Example
Solution
We assume that the average value of c is 1/2. The baud rate is then
Bandwidth
■ Although the actual band width of a digital signal is infinite, the effective BW is finite.
■ Baud rate determines the required band width for a digital signal.
■ Bandwidth(Range of frequencies) is proportional to the signal rate(baud rate).
■ Minimum BW is given by
■ If band width of a channel is given, the maximum data rate is given by
Baseline Wondering
■ In decoding the digital signal, receiver calculates the running average of the received signal power.
■ This average is Base line.
■ To determine the value of data element, the incoming signal power is evaluated against this baseline.
■ A long string of 0’s and 1’s can cause drift in the baseline and make it difficult for the receiver to decode correctly.
■ A good line coding scheme needs prevent baseline wondering.
D C Component
■ When the voltage level in a digital signal is constant for a while, spectrum creates very low frequencies .
■ These frequencies around zero is called D C Component.
■ Present problem for systems that can not pass low frequencies.
Eg: Telephone lines cannot pass frequencies below 200 HZ.
■ Need a good line coding scheme with no DC Component.
Self-Synchronization
■ To correctly interpret the signal received from the sender, the receiver’s bit interval must exactly match with sender’s bit interval.
■ If receiver’s clock is faster/slower, bit intervals are not matched and receiver might misinterpret the signals.
Continued. .
■ Since receiver’s bit duration is shorter, the receiver receives 110111000011.
■ Self synchronizing digital signal includes timing information in the data being transmitted.
■ This can be achieved by including transitions in the signal to alert the receiver beginning, middle and end of a pulse.
■ If receiver’s clock is out of synchronization, these points can reset the clock.
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?
Example
Solution
At 1 kbps, the receiver receives 1001 bps instead of 1000 bps.
At 1 Mbps, the receiver receives 1,001,000 bps instead of 1,000,000 bps.
Continued..
■ Built-in-error-detection:
Generated code should have
built-in-error-detecting capabilities to detect some or all the errors that occurred during transmission.
■ Immunity to noise and Interference
The code generated should be immune to noise and interference.
■ Complexity
Line Coding Schemes
• Line coding schemes are divided into five broad categories
•There are several schemes in each category.
Unipolar scheme
■ All signal levels are on one side of the time axis, either above or below.
Polar Schemes
■ Voltages are on both the sides of the time axis.
Voltage level for 0 +ve and Voltage level for 1 -ve Non return to Zero(NRZ)
■ In Polar NRZ encoding, we use two levels of voltage amplitude NRZ-L: (NRZ-Level)
■ The level of voltage determines the value of bit.
NRZ-I(NRZ-Invert)
The change or lack of change in level of the voltage determines the value of the bit.
bit 0=+ve to –ve transition & if next bit=0 no inversion bit 1= -ve to +ve transition .If next bit =1, invert.
■ Baseline wondering, synchronization and DC component problem in both variations.
Polar schemes (NRZ-L and NRZ-I)
A system is using NRZ-I to transfer 10-Mbps data. What are the average signal rate and minimum bandwidth?
Example
Solution
The average signal rate is S = N/2 = 500 kbaud.
The minimum bandwidth for this average baud rate is Bmin = S = 500 kHz.
Return to Zero(RZ)
■ To over come deficiencies of NRZ, RZ uses three voltage values: +ve, -ve and zero.
■ Signal change is not between bits but during the bit interval.
RZ
■ Signal goes to zero in the middle of each bit.
■ It remains there until the beginning of the next bit.
■ Disadvantage is , requires two signal changes to encode a bit ,therefore occupies more BW.
■ No DC Component problem but complexity as it uses
three voltage levels, which is more complex to create and discern.
■ Not used today because of these deficiencies.
Biphase(Manchester & Differential Manchester
)
■ The idea of RZ(Transition in the middle of bit) and idea of NRZ-L are combined into Manchester encoding.
■ In Manchester and differential Manchester encoding, the transition in the middle of the bit is used for
synchronization.
■ In Manchester encoding, bit is divided into two halves.
■ The voltage remains at one level during first half and moves to another level in the second half.
Differential Manchester Encoding
■ Combines the idea of RZ and NRZ-I.
■ There is a transition at the middle of the bit , but bit values are determined at the beginning.
■ If bit 0 Transition in the beginning bit 1 Transition in the middle Advantage:
1. Signal synchronizes itself.
2. Minimizes error rate and optimizes reliability.
Disadvantage:
1. Requires more bits than those in original signal.
Manchester and Differential Manchester
schemes
Bipolar schemes
■ There are three voltage levels +ve, -ve and 0.
■ The voltage level for one data element is at 0 while the voltage level of other elements alternate between +ve and –ve.
AMI(Alternate Mark Inversion)
■ The term Mark comes from telegraphy which means 1 .
■ So, AMI alternates 1 inversion. A Neutral zero voltage represents binary 0 and binary 1 are represented by
alternating +ve and –ve voltages.
Pseudo ternary scheme
■ Variation of AMI
■ 1 bit is encoded as a zero voltage
■ 0 bit is encoded as alternating +ve and –ve voltage.
■ Advantage is no DC component because long sequence of 1’s means voltage levels will be altered and long
sequence of 0’s means voltage level 0 only.