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ECE 4710: Lecture #11 1
Binary vs. Multi-Level
1 0 0 1 0 0 1 1
8-Bit Message: 10010011
t
5 V
Ts = 1 msec T0 = 8 Ts = 8 msec
R = (8/8 ms) = 1 kbps FNBW = 1/Ts = 1 kHz
Ts
T0
Binary Waveform
ECE 4710: Lecture #11 2
Binary vs. Multi-Level
8-Bit Message: 10010011
t
5 V3 V1 V
Ts = 2 msec T0 = 4 Ts = 8 msec D = (4/8 ms) = 500 sps
R = (8/8 ms) = 1 kbps FNBW = 1/Ts = 500 Hz
T
s
T0
L=4 Multi-Level WaveformSymbol
Key
00 = 0 V
01 = 1 V
10 = 3 V
11 = 5 V
1 00 1
0 0 1 1
Same Data Rate, One-Half BW
ECE 4710: Lecture #11 3
Binary vs. Multi-Level
8-Bit Message: 10010011
t
5 V3 V1 V
Ts = 1 msec T0 = 4 T = 4 msec D = (4/4 ms) = 1 ksps
R = (8/4 ms) = 2 kbps FNBW = 1/Ts = 1 kHz
Ts
T0
L=4 Multi-Level WaveformSymbol
Key
00 = 0 V
01 = 1 V
10 = 3 V
11 = 5 V
1 0 0 1 0 0 1 1
Same BW, 2 Data Rate
ECE 4710: Lecture #11 4
Binary vs. Multi-Level
Reduced BW OR increased data rate significant advantage for multi-level signal Why not do this 100% of the time?? Why not increase to L = 8 or L = 16 levels??
Primary disadvantage: for same S/N ratio a multi-level signal will have higher probability of bit errors compared to binary signal Reduced ability to accurately discriminate between
different signal levels
ECE 4710: Lecture #11 5
Binary vs. Multi-Level
1 0 0 1 0 0 1 1 t
5 VT
VS.5 V3 V1 V
T1 0
0 10 0 1 1
t
ECE 4710: Lecture #11 6
Channel Capacity
Shannon’s capacity formula
Use multi-level signal to decrease BW required S/N increases to maintain same capacity for same BER
User error coding to lower S/N requirement for same BER required bandwidth increases to handle additional coding bits while maintaining same capacity (data rate)
BW for S/N tradeoff is ** fundamental ** for all communication systems
)bps(1log2
N
SBC
ECE 4710: Lecture #11 7
Binary Line Coding
Line Codes : Binary 1’s and 0’s represented by a variety of serial-bit signaling formats
Two Major Categories
Non Return-to-Zero (NRZ)
» Signal waveform amplitude stays at one constant value for full duration of bit period
Return-to-Zero (RZ)
» Signal waveform amplitude returns to zero volt level for a portion of the bit period zero level portion is usually 0.5 Tb for “1”
t
A
Tb
01 0 1
t
A
Tb
0
1 0 1
ECE 4710: Lecture #11 8
Binary Line Coding
Four major sub-classifications based on the rules used to assign voltage levels to binary data (1/0) Unipolar Signaling : positive signaling has “1” = +A volts and “0” = 0
volts» Also called “On/Off Keying”
Polar Signaling : “1”= + A volts and “0” = A volts Bipolar (AMI) Signaling : binary “1” represented by alternating positive
and negative values while binary “0” is represented by constant zero volt level» Also called “Alternate Mark Inversion” = AMI
Manchester Signaling : “1” represented by positive/negative cycle in one bit period while “0” represented by negative/positive cycle» Also called “Split Phase Coding”
ECE 4710: Lecture #11 9
Common Line Codes
ECE 4710: Lecture #11 10
Common Line Codes
1 1 0 1 0 0 1
ECE 4710: Lecture #11 11
Shorthand Names
Book adopts shorthand naming convention that is common in industry Unipolar NRZ Unipolar Polar NRZ Polar Bipolar RZ Bipolar
Bipolar vs. Polar Polar NRZ is sometimes called Bipolar NRZ (Bipolar)
» Common in satellite communications» Book does NOT use this convention
Book uses telephone industry convention» T1 Bipolar RZ = Bipolar
ECE 4710: Lecture #11 12
Properties
Various line codes have advantages and disadvantages Signaling line code selected based on properties and
intended application Important properties
Self-synchronization» Enough timing information built-into code so bit synchronizers in
Rx can be designed to extract timing/clock signal from the code itself Clock signal needed to control sampling trigger in receiver
» Long series of binary 1’s or 0’s should NOT cause problem in recovery of clock signal
ECE 4710: Lecture #11 13
Properties
Important properties (continued) Probability of Bit Error
» Rx designed so that BER is low when signal is corrupted by ISI or channel noise
Spectrum/Bandwidth» Signal BW should be small relative to channel BW so no ISI» Spectrum suitable for baseband channels with AC or DC coupling
AC coupled channels like phone lines require line code signal PSD to have little or no energy at DC (f =0) If PSD has significant energy at DC then AC channel will
significantly attenuate signal, distort signal, and cause large amount of ISI
ECE 4710: Lecture #11 14
Properties
Important properties (continued) Error Detection
» Some line codes can have simple error detection built in» Channel codecs should be easy to implement for chosen line code
Transparency» Data protocol and line code designed so that every possible data
sequence is faithfully and transparently received» Code is NOT transparent if certain data sequences are reserved
for control purposesRandom data might accidentally generate control sequence
» Code is NOT transparent if long string of 1’s or 0’s result in loss of synchronization signalBipolar format is not transparent since long string of 0’s will
cause loss of clocking signal
ECE 4710: Lecture #11 15
Spectrum
PSD for deterministic waveform given previously as
Stochastic approach finds PSD for line code with random data sequence more realistic
Digital signal represented by
)( )( e.g. )]([|)(|
lim)(2
fRRT
fWf www
T
Tw PP
nn
ssn
a
T
tf
nTtfats
data random ofset }{
period symbol
shape pulse)(
where)()(
ECE 4710: Lecture #11 16
Spectrum
For unipolar NRZ line code :
General expression for PSD of digital signal is
F(f ) is FT of f (t) and R(k) is autocorrelation of the binary data given by
"0"for V 0
"1"for V and )(
n
n
b a
Aa
Tt
tf
k
Tfkj
ss
sekRTfF
fP 22
)(|)(|
)(
product ofy probabilit
symbol )( of level voltage
symbol of level voltage
th
th
th
where)()(1
knanaiiP
knkna
nnaI
iiiknn PaakR
ECE 4710: Lecture #11 17
Polar NRZ line code Possible levels are +A and A If data are independent (uncorrelated from bit to bit)
FT of pulse shape is
Polar NRZ Spectrum
!!041
41
)(41
)(41
)()(
0
21
21
)()0(
0
24
1
2
222
1
2
AAAAAAPaakR
k
AAAPaaR
k
iiknn
iinn
b
bb
b Tf
TfTfF
Tt
tfsin
)()(
ECE 4710: Lecture #11 18
Polar NRZ Spectrum
Substituting into2
222 sin
)(|)(|
)(
b
bb
k
Tfkj
ss Tf
TfTAekR
TfF
fP s
Normalized A = 1
A2