Chapter 4 Digital Transmission Line Coding Mapping Data symbols onto Signal levels Relationship between data rate in addition to signal rate
January, Ron, Morning Host; General Manager has reference to this Academic Journal, PHwiki organized this Journal Chapter 4 Digital Transmission Copyright © The McGraw-Hill Companies, Inc. Permission required as long as reproduction or display. 4-1 DIGITAL-TO-DIGITAL CONVERSION In this section, we see how we can represent digital data by using digital signals. The conversion involves three techniques: line coding, block coding, in addition to scrambling. Line coding is always needed; block coding in addition to scrambling may or may not be needed. Line Coding Line Coding Schemes Block Coding Scrambling Topics discussed in this section: Line Coding Converting a string of 1s in addition to 0s (digital data) into a sequence of signals that denote the 1s in addition to 0s. For example a high voltage level (+V) could represent a 1 in addition to a low voltage level (0 or -V) could represent a 0.
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Figure 4.1 Line coding in addition to 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 in addition to -V, 0 -> -V in addition to +V The ratio r is the number of data elements carried by a signal element. Relationship between data rate in addition to signal rate The data rate defines the number of bits sent per sec – bps. It is often referred to the bit rate. The signal rate is the number of signal elements sent in a second in addition to is measured in bauds. It is also referred to as the modulation rate. Goal is to increase the data rate whilst reducing the baud rate.
Figure 4.2 Signal element versus data element Data rate in addition to 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 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 in addition to 1 Solution We assume that the average value of c is 1/2 . The baud rate is then Example 4.1
Although the actual b in addition to width of a digital signal is infinite, the effective b in addition to width is finite. The maximum data rate of a channel (see Chapter 3) is Nmax = 2 × B × log2 L (defined by the Nyquist as long as mula). Does this agree with the previous as long as mula as long as Nmax Solution A signal with L levels actually can carry log2L bits per level. If each level corresponds to one signal element in addition to we assume the average case (c = 1/2), then we have Example 4.2 Considerations as long as choosing a good signal element referred to as line encoding Baseline w in addition to ering – a receiver will evaluate the average power of the received signal (called the baseline) in addition to use that to determine the value of the incoming data elements. If the incoming signal does not vary over a long period of time, the baseline will drift in addition to thus cause errors in detection of incoming data elements. A good line encoding scheme will prevent long runs of fixed amplitude.
Line encoding C/Cs DC components – when the voltage level remains constant as long as long periods of time, there is an increase in the low frequencies of the signal. Most channels are b in addition to pass in addition to 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 in addition to the receiver must have the same bit interval. If the receiver clock is faster or slower it will misinterpret the incoming bit stream. Figure 4.3 Effect of lack of synchronization
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 4.3 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 Noise in addition to interference – there are line encoding techniques that make the transmitted signal immune to noise in addition to interference. This means that the signal cannot be corrupted, it is stronger than error detection.
Line encoding C/Cs Complexity – the more robust in addition to resilient the code, the more complex it is to implement in addition to the price is often paid in baud rate or required b in addition to width. Figure 4.4 Line coding schemes Unipolar All signal levels are on one side of the time axis – either above or below NRZ – Non Return to Zero scheme is an example of this code. The signal level does not return to zero during a symbol transmission. Scheme is prone to baseline w in addition to ering in addition to DC components. It has no synchronization or any error detection. It is simple but costly in power consumption.
Figure 4.5 Unipolar NRZ scheme Polar – NRZ The voltages are on both sides of the time axis. Polar NRZ scheme can be implemented with two voltages. E.g. +V as long as 1 in addition to -V as long as 0. There are two versions: NZR – Level (NRZ-L) – positive voltage as long as one symbol in addition to negative as long as the other NRZ – Inversion (NRZ-I) – the change or lack of change in polarity determines the value of a symbol. E.g. a 1 symbol inverts the polarity a 0 does not. Figure 4.6 Polar NRZ-L in addition to NRZ-I schemes
In NRZ-L the level of the voltage determines the value of the bit. In NRZ-I the inversion or the lack of inversion determines the value of the bit. NRZ-L in addition to NRZ-I both have an average signal rate of N/2 Bd. NRZ-L in addition to NRZ-I both have a DC component problem in addition to baseline w in addition to ering, it is worse as long as NRZ-L. Both have no self synchronization &no error detection. Both are relatively simple to implement.
A system is using NRZ-I to transfer 1-Mbps data. What are the average signal rate in addition to minimum b in addition to width Solution The average signal rate is S= c x N x R = 1/2 x N x 1 = 500 kbaud. The minimum b in addition to width as long as this average baud rate is Bmin = S = 500 kHz. Note c = 1/2 as long as the avg. case as worst case is 1 in addition to best case is 0 Example 4.4 Polar – RZ The Return to Zero (RZ) scheme uses three voltage values. +, 0, -. Each symbol has a transition in the middle. Either from high to zero or from low to zero. This scheme has more signal transitions (two per symbol) in addition to there as long as e requires a wider b in addition to width. No DC components or baseline w in addition to ering. Self synchronization – transition indicates symbol value. More complex as it uses three voltage level. It has no error detection capability. Figure 4.7 Polar RZ scheme
Figure 4.19 Two cases of B8ZS scrambling technique HDB3 substitutes four consecutive zeros with 000V or B00V depending on the number of nonzero pulses after the last substitution. If of non zero pulses is even the substitution is B00V to make total of non zero pulse even. If of non zero pulses is odd the substitution is 000V to make total of non zero pulses even. Figure 4.20 Different situations in HDB3 scrambling technique
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