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Chapter 3: Line Codes and Their Spectra

Chapter 3: Line Codes and Their Spectra. Types of Line Codes Comparison of Line Codes PSD of Line Codes. Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University. Analog Input Signal. Sample. X. Quantize.

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Chapter 3: Line Codes and Their Spectra

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  1. Chapter 3: Line Codes and Their Spectra • Types of Line Codes • Comparison of Line Codes • PSD of Line Codes Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University

  2. Analog Input Signal Sample X Quantize ADC XQ Encode Xk Line Code x(t) PCM signal Line Codes in PCM • The output of an ADC can be transmitted over a baseband channel. • The digital information must first be converted into a physical signal. • The physical signal is called a line code. Line coders use the terminology mark to mean binary one and space to mean binary zero.

  3. Line codes 1 1 0 1 0 0 1 BINARY DATA (a) Punched Tape Mark (hole) Mark (hole) Mark (hole) space Mark (hole) space space Volts A 0 (b) Unipolar NRZ Tb Time A (c) Polar NRZ 0 -A A (d) Unipolar RZ 0 A (e) Bipolar RZ 0 -A A (f) Manchester NRZ 0 -A Binary Signaling Formats

  4. Goals of Line Coding • A line code is designed to meet several goals: • Self-synchronization. • The ability to recover timing from the signal itself. • Long series of ones and zeros could cause a problem. • Low probability of bit error. • The receiver needs to be able to distinguish the waveform associated with a mark from the waveform associated with a space, even if there is a considerable amount of noise and distortion in the channel. • Spectrum that is suitable for the channel. • In some cases DC components should be avoided if the channel has a DC blocking capacitance. • The transmission bandwidth should be minimized.

  5. Physical Waveform Digital Data Line Coder Line Coder • The input to the line encoder is a sequence of values ak that is a function of a data bit or an ADC output bit. • The output of the line encoder is a waveform: • Where p(t) is the Pulse Shapeand Tbis the Bit Period • Tb =Ts/n for n bit quantizer (and no parity bits). • Rb =1/Tb=nfs for n bit quantizer (and no parity bits). • The operational details of this function are set by the particular type of line code that is being used.

  6. Types of Line Codes • Each line code is described by a symbol mapping function ak and a pulse shapep(t): • Categories of line codes: • Symbol mapping functions (ak). • Unipolar • Polar • Bipolar (a.k.a. alternate mark inversion, pseudoternary) • Pulse shapes p(t). • NRZ (Nonreturn-to-zero) • RZ (Return to Zero) • Manchester (split phase)

  7. Unipolar NRZ Line Code • The unipolar nonreturn-to-zero line code is defined by the unipolar mapping: • where Xk is the kth data bit. • In addition, the pulse shape for unipolar NRZ is: • Where Tb is the bit period. Hard to recover symbol timing when long string of 0s or 1s. Note the DC component This means wasted power! 0 1 1 1 1 0

  8. Unipolar RZ Line Code • The unipolar return-to-zero line code has the same symbol mapping but a different pulse shape than unipolar NRZ: Long strings of 1’s no longer a problem. However strings of 0’s still problem. Pulse of half the duration of NRZ requires twice the bandwidth! 0 1 1 1 1 0

  9. Polar Line Codes • Polar line codes use the antipodal mapping: • Polar NRZ uses NRZ pulse shape. • Polar RZ uses RZ pulse shape. No DC component, so more energy efficient. 0 1 1 1 1 0 Polar NRZ Now we can handle long strings of 0’s, too. Polar RZ

  10. 1 0 1 1 1 0 Manchester Line Codes • Manchester line codes use the antipodal mapping and the following split-phase pulse shape: • Easy synchronization and better spectral characteristics than polar RZ.

  11. 1 0 1 1 1 0 Bipolar (RZ) Bipolar Line Codes • With bipolar line codes a space is mapped to zero and a mark is alternately mapped to -A and +A: • Also called pseudoternary signalling and alternate mark inversion (AMI). • Either RZ or NRZ pulse shape can be used.

  12. Comparison of Line Codes • Self-synchronization: • Manchester codes have built in timing information because they always have a zero crossing in the center of the pulse. • Polar RZ codes tend to be good because the signal level always goes to zero for the second half of the pulse. • NRZ signals are not good for self-synchronization. • Error probability: • Polar codes perform better (are more energy efficient) than Unipolar or Bipolar codes. • Channel characteristics: • We need to find the PSD of the line codes to answer this ...

  13. Power Spectra for Binary Line Codes • PSD can be calculated using the autocorrelation function: • A digital signal is represented by • f(t) - Symbol Pulse shape; Ts - Duration of one symbol; • Binary signaling : Ts= Tb , Multilevel signaling: Ts= lTb • PSD depends on: (1) The pulse shape used (2) Statistical properties of data expressed by the autocorrelation function • The PSD of a digital signal is given by:

  14. PSD for Polar NRZ Signaling Possible levels for the a’s : +A and -A

  15. PSD for line codes Unipolar NRZ Polar NRZ Bit rate: R=1/Tb

  16. PSD for line codes Unipolar RZ Bipolar RZ Manchester NRZ Bit rate: R=1/Tb

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