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

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. ADC PCM signal Sample Quantize Analog Input Signal Encode Line Code X XQ Xk x(t)

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

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.

Line Coder Line Coder Digital Data Physical Waveform 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 Shape and Tb is 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.

Types of Line Codes Each line code is described by a symbol mapping function ak and a pulse shape p(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)

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! 1 1 1 1

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! 1 1 1 1

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. 1 1 1 1 Polar NRZ Now we can handle long strings of 0’s, too. Polar RZ

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

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 ...

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:

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

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

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