Linecodes and scrambling

IET, NTNU Digital Communication, Line codes and scrambling Presentation in course TTT4130 Digital Communication Line codes and scrambling  Curriculum found in Barry, Lee, Messerschmitt  Chapter 19 (19.1, 19.3 and 19.5)  IET, NTNU
Digital Communication, Line codes and scrambling
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Line coding
The purpose of a line code is to match the output signal
to the channel for baseband transmission. The line coder
consists of a mapping of bits into symbols (nonlinear)
and a pulseshaping filter (linear).
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Properties of line codes
•
Power spectrum
•
Timing recovery properties
•
DC-balance (zero DC component)
•
Redundancy
•
Linearity
•
Polarity independence
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Efficiency and redundancy
Maximum bitrate:
R = fb · lb(L) (lb = log2)
L: no of output symbol levels
fb: symbol rate in symb/s
B: actual bitrate in bit/s
Code ef ficiency:
= B/R
Redundancy: r = 1-

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Example, 4B3T code
The 4B3T code is coding 4 input bits to 3 three-level
symbols (24 = 16 combinations of input and 33 = 27 potential output
combinations).
Maximum bitrate: R = fb · lb 3
Actual bitrate: B = fb · 4/3
Code ef ficiency:
= R/B = 4/(3·lb 3) = 0.84
Redundancy: r = 1- 0.84 = 0.16
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Linear codes
Input symbols are ak = ±1 and pulseshapes are de fined in Fig 19.2
Biphase has zero DC component in each pulse
RZ and NRZ may have a DC component
Biphase and RZ has transitions in each pulse ): good timing properties
NRZ may have long sequences of +1 or -1 ): poor timing properties
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Coded sequences
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AMI code (Alternate Mark Inversion)
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ak=0 bk=0 ±1bk=1( alternating
1and+1)   The AMI code may be generated
as shown in the figure:
bk=0: ck=ck1ak=0 bk=1: ck
ck1ak=±1 ckchanges between 0 and 1 each time bk=1 + zero DC component
- may contain long sequences of 0 (poor timing recovery)
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Digital Communication, Line codes and scrambling
DC-balance
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Most transmission systems will be a.c. coupled. In metallic
cables a transformer is used to avoid overvoltages. A.c. coupling
may also be used due to implementation aspects. A.c. coupling
means that d.c. is filtered out in a high-pass filter as shown in
Fig 19.1a. This causes a slowly varying InterSymbol Interference
that is denoted baseline wander . A Nyquist channel + a high pass
filter in cascade will give a model for ISI as shown in Fig 19.1b.
 = 2RC
= exp(- T/)
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Running digital sum
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pk=p(kT)=0 k<0 1 k=0
T/k>0     By assuming
= 1, the overall time discrete impulse response may be
approximated:
Output signal at time k:
yk= am m=

 pkm=akT am m=
k1  =akT Sk1 Intersymbol interference at time k:
Running digital sum, RDS:
ISI(k)=
T Sk
1Sk= am m=
k  For a balanced line code RDS is bounded, and the DC content is zero.
max( ISI)=T min( Sk1), max( ISI)
for independent ak IET, NTNU Digital Communication, Line codes and scrambling  11Impulse response for DC cutoff, simulation example illustrating baseline wander  Cosine rolloff 100% + H(f)=j j+2
0.02 3 dB cutoff frequency:  0.02/ T
=T/(2
·0.02) =7.96T
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Eye curve for NRZ code with DC cutoff
Cosine rolloff 100% + H(f)=j j+2
0.02 NRZ is an unbalanced
line code ): serious
baseline wander
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Eye curve for AMI code with DC cutoff
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Cosine rolloff 100% + H(f)=j j+2
0.02 AMI is a balanced
line code ): small ISI
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Power spectrum of a line code
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X(t)= ak k=

 g(tkT) SX(f)=1 TSa(ej2
fT)G(f)2Transmitted signal:
Power spectrum:
Sa(z) : Time discrete power spectrum of sequence {ak}
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Digital Communication, Line codes and scrambling
Power spectrum NRZ code
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Digital Communication, Line codes and scrambling
Power spectrum Biphase
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Power spectrum AMI code
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Power spectrum for three simple codes
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NB: All codes
have equal
average power
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Comparison of simple codes
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Code
Balanced
Timing properties
Minimum bandwidth
RZ
no
good
1/(2T)
NRZ
no
poor
1/(2T)
Biphase
yes
good
1/T
AMI
yes
poor
1/(2T)
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Ternary (3-level) codes
An kBnT block code is coding k bits into n 3-level symbols
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One alternative of a 4B3T code
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Binary codes
Binary codes are relevant for optical transmission.
The number of balanced codewords of length n is given by:
N=n! (n/2)! (n/2)!Corresponding codes are shown in the table
Due to low ef ficiency, nBmB codes are used instead, where
m = n +1 (e.g. 5B6B)
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Partial response
F(z)
ck = ±1
yk
F(z) = (1 - z-1)m · (1 + z-1)n
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Alternatives of partial response
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Type partial response
n =
m =
F(z)=
Dicode
0
1
1-z-1
Duobinary
1
0
1+z-1
Modi fied duobinary
1
1
(1+z-1)(1- z-1)=1- z-2
1z1=1exp(j2
fT)=2jexp(j
fT)sin(
fT), ) : zero at f=0 1+z1=1+exp(j2
fT)=2exp(j
fT)cos(
fT), ) : zero at f=1/(2 T) IET, NTNU
Digital Communication, Line codes and scrambling
Duobinary partial response
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ck ck-1 Output yk -1 -1 -2 -1 1 0 1 -1 0 1 1 2 yk = ck + ck-1
For duobinary, a two-level signal is coded into three
levels. Modi fied duobinary and dicode will also have
three-level output for binary input. Other alternatives
of partial response will have more output levels.
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Spectral shaping by partial response
IET, NTNU Digital Communication, Line codes and scrambling  27Decoding of partial response ? ck - ck-1 ck-1 ck - ck-1ck - ck-1 ck-1 IET, NTNU
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Precoding of partial response (duobinary)
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z-1
z-1
+

0 to -1
1 to +1
Precoder
bk = 0,1
dk = 0,1
ck = ±1
ak
ˆ b kConvert to
bipolar
Duobinary
coding
3-level
decision
bk=0dk=dk1ck=ck1ak=ck+ck1=±2ˆ b k=0 bk=1dk
dk1ck
ck1ak=ck+ck1=0ˆ b k=1 Decoding depends only on current received signal sample ):
no error propagation.
Precoding may be used also for modi fied duobinary and dicode.
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Scrambling
•
Most transmission systems are based on an assumption of random input data ): statistically independent bits and p(“0”) = p(“1”) = 1/2
•
Practical input data often differ from this assumption and may for instance contain long strings of ones or zeroes
•
Scrambling is a way to ensure approximately random data
•
Scrambling is based on pseudorandom sequences generated by linear feedback shift registers.
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Linear feedback shift register
Number of states in a shift register of length n: 2n
The output sequence is periodic, and for a maximum length shift register the period is: 2n-1
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Frame-synchronized scrambler
Assuming error free transmission:
ˆ b k=ˆ c k
xk=ck
xk=bk
xk
xk=bk - The transmitter and receiver shift registers have to be synchronized
+ One bit error per transmission error
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Self synchronized scrambler
Assuming error free transmission:
ˆ b k=ˆ c k
ˆ d k=ck
dk=bk
dk
dk=bk + Automatic synchronization
- Minimum three bit errors per transmission error
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Applications of scrambling
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Echo cancelling
–
Two different scramblers, one for each direction of transmission
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Synchronization
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Adaptive equalization
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Interference cancellation
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...
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Maximum length shift registers
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Table of maximum length shift registers