sks07en 11-12 coding and modulation[1]

7/24/2019 SKS07en 11-12 Coding and Modulation[1]

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7. Coding and

Modulation

FER-Zagreb, Satellite communication systems 2011/12


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Topics

Introduction Convolutional coding

Reed-Solomon coding

Concatenated coding

FEC Forward error correction

Digital modulation

PCM Pulse code modulation

QAM Quadrature amplitude modulation ISI intersymbol interference

Modulation spectral efficiency

BER bit error rate



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Introduction

Coders are part of transmitter systems and decoders arepart of receiver systems.

Signal transmission is subject to error or interference.

There are error detecting and correcting codes.

Parity (redundant) bits are introduced into the knowninformation bits. This reduces the data speed.

The number of parity bits necessary depends oninterference in the communication channel and interference.

Adequate decoder must exists on receiver side. Decoderdepends on the coding method used on transmitter side.



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Introduction In modulation process, one or more parameters of the

auxiliary signal is changed. The auxiliary signal is called thecarrier.

Signal which contains the information is called the modulationsignal. It controls the changes of carrier.

The result of modulation procedure is modulated signal. Whole procedure is performed in modulator.

Reverse procedure to modulating is demodulating at receiver.

Difference between analog and digital modulations is in the

modulation signal. With digital modulations, modulationsignal is either 0 or 1.



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Convolutional coding Code has three main characteristics:

Code length number of bits in a code word

Code dimension number of information bits in a codeword

Code distance number of bits necessary to move fromone to other code word

Convolutional coding can correct error bits which gives codinggain to the system.

Codes have three parameters:

n number of output bits

k number of input bits

m number of memory registers

Ratio k/n= Ris a code rateFER-Zagreb, Satellite communication systems 2011/12


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Convolutional coding Usually kand nhave values between 1 and 8, and code rate Rhas valuesfrom 1/8 to 7/8.

There can be 2 to 10 memory registers (m).

Kis the number of bits in coder memory which affects the creation of noutput bits:

K = k (m - 1)

Convolutional coding is performed with shift registers (K) and nmodulo 2adders.

Larger Kmeans more influence of the previous bits on the output codeword.

Example K= 3, n= 2

For every bit in register, the output changes n= 2 code bits (u1and u2) Code rate k/n= 1/2 Every output bit is a function of input bit (left state of register) and two

previous bits (right states of register).FER-Zagreb, Satellite communication systems 2011/12


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Convolutional coding

Input bitm

Secondcode bit

First

code bitOutputword

K = 3, n= 2



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Convolutional codingViterbi Decoder Viterbi decoder corrects the errors received during

transmission.

Decoding is more complicated procedure than encoding and

limits the communication speed. Integer number Kis the number of frames processed in

every step.

Input to decoder can be

Real number (positive real number is logical zero andnegative real number is positive one)

0 i 1 -hard decision

soft decision integer between 0 and 2b-1; bis aparameter of soft decision



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Input value Decision

0 Most probable zero1 Second most probable zero

2 Third most probable zero

3 Least probable zero

4 Least probable one5 Third most probable one

6 Second most probable one

7 Most probable one

Decision for b= 3



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Table shows typical values of decoding gain

Code rate EB/N0required for BEP = 10-6(dB) Decoding gain (dB)

1 10.5 0

7/8 6.9 3.6

3/4 5.9 4.6

2/3 5.5 5.01/2 5.0 5.5


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Reed-Solomon coding As convolutional coding, RS coding adds redundant bits and creates codewords which enable correcting errors in decoder. Difference from convolutional coding is that RC encodes bit blocks instead

one bit. RS coding is eight times more faster than convolutional coding. Input bits are first packed into small blocks of ksymbols which are then

packed in super blocks with nsymbols by adding redundant bits. Transmission of information is decreased by code rate R,

1/R= n/k

where nis number of output bits

kis number of input bits

RS decoder can correct tsymbols of the code word according to

2t= n -k



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Reed-Solomon coding


RS(204,188, T=8) has 16 redundant bits and possibility to correct 8 bits.

2t= nk = 204 - 188 = 16t = 8

One bit is used for synchronization and 187 bits contain information. RS(204,188, T = 8) is shortened code from original RS(255, 239, T = 8). Used in DVB-S.


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Concatenated coding Concatenated (joined) coding for DVB-S standard has two codes: outer

(RS) and inner (convolutional). Inner decoder corrects errors at the output of demodulator, while outer

decoder corrects occasional bursts of errors created by inner decoder.

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FEC Forward Error Correction FEC is a digital signal processing which increases the reliability of data by

introducing known structure into data stream before transmission.

The known structure enables the receiving system detection and possiblecorrection of errors in the channel or receiver.

Correction of data means that it is not necessary to send the information

again (useful with real time information). Original data is consisting of nbits. Encoder introduces redundant (parity)

bits r, increasing total number of bits to n + rof code word.

On the receiving end, decoder extracts the original data.

The code rate is defined as

where ris the number of redundant bits added to ninformation bits.


rn

n

+=


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FEC Forward Error Correction The bit rate at the encoder input is Rb. At output, the rate is greater and equal to Rc:

b

c

RR =

FER-Zagreb, Satellite communication systems 2011/12 14


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FEC Forward Error Correction

6,3encoder

Information

...010I011I110... 101 010I000 011I000 110I

Code word

Parity bits Information bits



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DigitalInformation

input

Digital

Informationoutput

n, n+rencoder

n, n+r

decoder

modulator

demodulator

channel

noise

Code bits estimationInformation bits estimation

Information bits

d1, d2,..., dk

d1, d2,..., dk u1, u2,..., uk

u1, u2,..., uk


Code bits


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Code measure is redundancy, or r/n.

Codes with high redundancy have relatively little information per codebit. Codes with little redundancy have fast code rate (close to 1) andcarry more information per code bit.

High redundancy has advantage that it lowers the possibility of losing theoriginal data during transmission. Disadvantage of high redundancy isthat usually requires larger bandwidth or introduces delay.

For the communication in real time, code rate must be increased byfactor 1/(n+r) to avoid decrease in data throughput. Furthermore, it isnecessary to increase the bandwidth by factor n/n+r(for modulation).

If communication is not in real time, delay can be introduced but not theincreased bandwidth.



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FEC Forward Error Correction Quality parameter BER (bit

error rate) vs ratio of S/N waterfall.

When S/N increases, BERdecreases system performsbetter

Coded system (on figure) has100 times smaller BER incomparison to the non codedsystem for same S/N.

Or, coded system has same BER

as non coded for lower S/N. Tedifference is called coding gain(4 dB in figure).

Smaller necessary S/N needssmaller antennas, lowertransmitting power, cheaper

receivers, ...

BER

10-2

10-4

S/N [dB]8 12

Coding gain

non codedcoded

Direction of improvementregarding errors



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Digital modulationASKAmplitude Shift Keying With ASK, the amplitude of carrier is changed according to the

modulation signal in a way that the carrier exists when modulation signalis equal to 1 and it does not exists if modulation signal is equal to 1.

This modulation is also called OOK (On-Off Keying).

Modulated signal is obtained by modulating the carrier signal (withfrequency fc) with modulating signal with frequencyfm):

Ideal ASK has infinitive spectrum. It is therefore necessary to shapepulses to narrow the frequency bandwidth.

Disadvantage of ASK modulation is that S/Nratio is not same for 1 andfor 0. It also needs different powers for those two states.

Break in communication is read as 0.

( )ASK1 2 2

cos cos cos 3 ... .2 3

cm c m mu t U t t t

= + +



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Digital modulation


ASKAmplitude Shift Keying


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Digital modulation FSK Frequency Shift Keying With FSK, the frequency of carrier is changed discretely according to the

modulation signal.

The simplest FSK is the BPSK or binary FSK with two carrier frequencies.

Examples: MSK Minimum Shift Keying with modulation index of 0.5

GMSK Gaussian MSK (mobile telephony)

FSK modulation can be achieved with two ASK signals, having frequenciesf1i f

2.

Demodulation of ASK is much easier than demodulation of FSK.



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Digital modulation

Modulation index is equal tothe ratio of frequency deviationfand modulation frequencyfm

Frequency deviation is

f0 =fc- ff1 =fc+f

fc carrier frequency

F

m

fm

f

=

1 0

2

f ff

=


FSK Frequency Shift Keying


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Digital modulation PSK Phase Shift Keying With PSK, the phase of carrier is changed in regard to the modulation

signal. The modulation phase can have two or more different, previouslydetermined phases.

PSK modulation can also be obtained by two ASK signals, similar to FSK.The difference is that with PSK, this two signals must be in quadrature

relation. PSK signal is equal to

mis modulation phase which can be

For M= 2, and c= 0, modulation phases will be 0 and , and for c= 1,phases will be /2 and 3/2. This modulation is called BPSK or Binary PSK.

Usually 0or 0 represents state 1 and or 180 represents 0.

( ) ( ) [ ]PSK cos cos cos sin sincm c m cm m c m cu t U t U t t = + =

( )2, 0,1, 2,... 1; 0,1.

m

n cn M c

M

+

= = =



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Digital modulation


PSK Phase Shift Keying


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Digital modulation

BPSK is resilient to interference but has small spectral efficiency.

For M= 4, there are 4 modulation phases making QPSK. Each state of QPSKrequires two bits while BPSK requires one bit.

QPSK demands more memory, and the possibility of error is higher. Spectralefficiency is higher, that is, it is possible to transmit two times moreinformation in a communication channel.

BPSK QPSKGray code

( ) ( )QPSK cos ( )sin .c cu t I t t Q t t =



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PCM Pulse Code Modulation With PCM modulation,

amplitude of analog signal issampled and quantized in orderto realize binary code.

PCM requires AD converter.The speed of sampling must beat least two times larger thanthe analog frequency:

fs >= 2fc

Quantization level willdetermine the accuracy ofanalog signal. Mode accurateconversion requires morememory.

Demodulation is similar tomodulation.

Receiver needs DA converter.



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QAM Quadrature amplitude modulation

QAM is a procedure where the amplitudes of two carriers are modulated.The phase difference between them is 90.

QAM can be both analog and digital.Analog QAMis similar to AM.

Digital QAMis used more often than analog QAM.

It has two modulation signals I(t) andQ(t)which are in relation

QPSK is actually a special case of QAM.

Difference is that QPSK has no amplitude modulation while QAM has. Depending on the quantization level, there could be 4-QAM, 16-QAM, 64-

QAM.

More states means more possibility of error.

( ) ( )QAM cos sin .c cu I t t Q t t =



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QAM Quadrature amplitude modulation



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ISI Intersymbol interference


When rectangular pulses pass through the frequency band limited channel,they spread in time, and pulse from each symbol will be spread into the

time interval of adjacent (next) pulse. This leads to intersymbolinterference. ISI can also appear from multipath propagation.

The obvious solution for lowering ISI is increasing the frequencybandwidth.


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ISI Interymbol interference


Modern communication

systems are working withminimum bandwidth.

Unwanted emission outsidebandwidth should be 40 dB to80 dB lower than in its own

channel. Since it is difficult to achieve

it in RF band, pulse shapingis done in baseband or at MF.

Figure shows frequency

response (above) andimpulse response (below) ofraised-cosine filter withvarious roll-off factors.


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Modulation spectral efficiency Modulation spectral efficiency is ratio of the transmitted bit rate Rc and

bandwidth occupied by the carrier.

The bandwidth occupied by the carrier depends on spectrum of themodulated carrier and filtering. Filtering is used for lowering theinterference to adjacent carriers.

ISI-free transmissions can be achieved with raised cosine filter.

Roll-off factor will determine the bandwidth.

For a raised cosine filter, the bandwidth Boccupied by the carrier is:

where TSis the symbol duration

Spectral efficiency for M-ary modulation is equal to

For roll off factor = 0.35, required bandwidth is 1.35/TS, and spectral

efficiencies (bit/s/Hz) are: 0.7 for BPSK, 1.5 for QPSK and 2.2 for 8PSK.FER-Zagreb, Satellite communication systems 2011/12

( ) ( )Hz/1 STB +=

( ) ( ) ( )bit/s/Hz

1

log

1

2

+=

+==

MTR

B

R Scc


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BER bit error rate Analog communications mostly use mean signal over mean noise (S/N) as

a quality parameter. In analog communications, waveform can be imagined as signal with

infinitely long duration and not divided in time, therefore with unlimitedamount of energy. It has final mean power and infinitive energy. Thereforepower is useful parameter for analog communications.

With digital communications, symbols are transmitter in a part of time TS. Ifonly one symbol is observed, mean power in all the time intervalapproaches zero. Therefore, power is not a satisfactory parameter fordigital systems.

In digital communications, more often is usedEb/N0, or normalized version

of signal and noise:

whereEbis energy per bit, N0is thermal noise in 1 Hz bandwidth, Ris thedata speed in the system andBTis the frequency bandwidth.


T

b

B

R

N

E

N

S

0

=


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BER bit error rate Symbol energy, or power integrated in time Tsis much more useful

parameter describing digital wave form.

Important characteristic of digital communication systems is BER, ornumber of bit errors in regard to E

b

/N0

.

LargerEb/N0 means smaller BER. System is adequate if BER is at least 10-6.

b

0

J Ws=

W/Hz Ws

E

N=



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BER bit error rate Bit error rate (BER) measures performance of demodulator by counting the

number of bits in error, nin a stream of Nreceived bits: BER = n/N

BER constitutes a nestimate of the bit error probability (BEP). A level ofconfidence is associated with this estimate, as follows:

63% level of confidence is obtained for k= 1 and 95% for k= 2. If n=100 errors within N= 105bits, with 63% confidence.

Carrier phase (phase shift) changes under the influence of noise lead toerrors in identification of received symbols, and bits.

Symbol error probability (SEP) is probability of a symbol being detected in

error (bit error probability is the probability of bit being detected in error). For two state modulation BEP = SEP, but for four state modulation, where

phase states follow Gray code, BEP = SEP/2.

In general


N

nk=BERBEP

43 1010BEP =

2forMlog/SEPBEP 2 = M


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BER bit error rate

Figure shows theoretical biterror probabilities (BEP) fordifferent modulations.

Bit error rate (BER) measuresperformance of demodulator by

counting the number of bits inerror, nin a stream of Nreceived bits:

BER = n/N

FER Zagreb Satellite communication systems 2011/12

sks07en 11-12 coding and modulation[1]

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