UNIT I
PULSE MODULATION
1. Define Nyquist rate
Let the signal be band limited to W Hertz. Then Nyquist rate
is given as
Nyquist rate =2W samples/sec
Aliasing will not take place if the sampling rate is greater than
Nyquist rate.
2. What is meant by aliasing effect?
Aliasing effect takes place when the sampling frequency is less
than Nyquist rate. Under such condition the spectrum of the sampled
signal overlaps with itself. Hence higher frequencies take the form of
lower frequencies. This interference of the frequency components is
called aliasing effect.
3. State sampling theorem.
Sampling theorem states that, a band limited signal of finite
energy which has no frequency components higher than W Hz is
completely described by specifying the values of the signal at instants
of time separated by 1/2W seconds.
4. Mention two merits of DPCM.
(i) Bandwidth requirement of DPCM is less compared to PCM.
(ii)Quantization error is reduced because of prediction filter.
(iii) No of bits used to represent one sample value are also reduced
compared to PCM.
5. What is the main difference in DPCM and DM?
DM encodes the input sample by only one bit. It sends the
information about +δ and –δ (ie) step rise or fall.DPCM can have
more than one bit for encoding the sample. It sends the information
about difference between actual sample value and predicted sample
value.
6. How the message can be recovered from PAM?
The message can be recovered from PAM by passing a PAM
signal through reconstruction filter. The reconstruction filter integrates
amplitudes of PAM pulses. Amplitude smoothing of the reconstructed
signal is done to remove amplitude discontinuities due to pulses.
7. Write an expression for bandwidth of binary PCM with N messages
each with a maximum frequency of fm Hz.
If v numbers of bits are used to code each input sample then
bandwidth of PCM is given as
BT≥ N.v.fm
Here v.fm is the bandwidth required by one message.
8. How is PDM wave converted into PPM systems?
The PDM signal is given as a clock signal to monostable
multivibrator.The multivibrator triggers on falling edge. Hence a PPM
pulse of fixed width is produced after falling edge of PDM pulse.PDM
represents the input signal amplitude in the form of width of the pulse.
A PPM pulse is produced after this width of PDM pulse. In other
words the position of the PPM pulse depends upon the input signal
amplitude.
9. Mention the use of adaptive quantizer in adaptive digital waveform
coding schemes.
Adaptive quantizer changes its step size according to variance
of the input signal. Hence quantization error is significantly reduced
due to adaptive quantization.ADPCM uses adaptive quantization. The
bit rate of such schemes is reduced due to adaptive quantization.
10. What do you understand from adaptive coding?
In adaptive coding, the quantization step size and prediction
filter coefficients are changed as per the properties of the input signal.
This reduces the quantization error and no of bits used to represent the
sample value. Adaptive coding is used for speech coding at low bit
rates.
11. What is meant by quantization?
While converting the signal value from analog to digital
quantization is perfomed.The analog value is assigned to the nearest
digital level. This is called quantization. The quantized value is then
converted to equivalent binary value. The quantization levels are fixed
depending upon the number of bits. Quantization is every analog to
digital conversion.
12. The signal to quantization noise ratio in a PCM system depends on
…………….
The signal to quantization noise ratio in a PCM is given as
(S/N) dB≤ (4.8+6v) dB
Here v is the no of bits used to represent samples in PCM.Hence
signal to quantization noise ratio in PCM depends upon number of bits
or quantization levels.
13. For the transmission of normal speech signal in the PCM channel
needs the BW of………….
Speech signals have the maximum frequency of
3.4kHz.Normally 8 bits PCM is used for speed. The transmission
bandwidth of PCM is given as
BT ≥ vW
≥ 8x3.4 kHz
≥ 2.72 kHz
14. It is required to transmit speech over PCM channel with 8 bit
accuracy. Assume the speech in baseband limited to 3.6 kHz.
Determine the bit rate
The signaling rate in PCM is given as
r= vfs
Here v=8
The maximum signal frequency is W= 3.6 kHz. Hence
minimum sampling frequency is
fs =2W=2x3.6kHz=7.2 kHz
r =8x7.2x103
=57.6k bits/sec
15. What is meant by adaptive delta modulation?
In adaptive delta modulation, the step size is adjusted as
per the slope of the input signal. Step size is made high if slope of the
input signal is high. This avoids slope overload distortion.
16. What is the advantage of delta modulation over pulse modulation
Schemes?
Delta modulation encodes one bit per sample. Hence
Signaling is reduced in DM.
17. What should be the minimum bandwidth required to transmit a
PCM channel?
The minimum transmission bandwidth in PCM is given as
BT = vW
Here v is the no of bits used to represent one pulse.
W is the minimum signal frequency.
18. What is the advantage of delta modulation over PCM?
Delta modulation uses one bit to encode one sample. Hence
bit rate of delta modulation is low compared to PCM.
19. Define Pulse amplitude modulation.
The amplitudes of regularly spaced pulses are varied in
proportion to the corresponding sample values of a continuous
message signal is called PAM. In PAM, the message signal is
multiplied by a periodic train of rectangular pulses.
20. What is aperture effect?
The distortion caused by the use of pulse amplitude
modulation to transmit an analog information bearing signal is
referred to as the aperture effect.
21. Define Quantization noise.
The use of quantization introduces an error defined as
the difference between the input signal m and the output signal v.The
error is called quantization noise.
22. Define Pulse position modulation.
The position of the pulse relative to its unmodulated
time of occurrence is varied in accordance with a message signal.
23. What are the two limitations of Delta modulation?
1) Slope overload distortion
It occurs due to limited step size and fast variations in the
signal
2) Granular noise
It occurs due to too large step size and very small amplitude
variations in the input signal.
24. Why compressor are used in PCM?
(i) With linear quantization the signal to quantization noise
reduces at low signal levels.
(ii) Compression uses nonlinear quantization. It improves
the signal to quantization noise ratio at low signal levels.
25. What should be the pass band for antialiasing and smoothing
filters used with pulse modulation and demodulation systems?
(i) Antialiasing filter used before sampling. It should band
limit the signal to maximum signal frequency if W Hz.
Hence its pass band should be W Hz.
(ii) Smoothing filter is used after reconstruction or
interpolation. It should successfully pass all the
frequencies of 0 to W Hz and block frequencies greater
than W Hz
26. Name the types of uniform quantizer?
1. Mid tread type quantizer.
2. Mid riser type quantizer.
27. What is the disadvantage of uniform quantization over the nonuniform quantization?
SNR decreases with decrease in input power level at the uniform
quantizer but non-uniform quantization maintains a constant SNR for
wide range of input power levels. This type of quantization is called
as robust quantization.
28. What do you mean by companding? Define compander.
The signal is compressed at the transmitter and
expanded at the receiver. This is called as companding The
combination of a compressor and expander is called a compander.
29. What is the need for speech coding at low bit rates?
The use of PCM at the standard rate of 64 Kbps demands a
high channel bandwidth for its transmission ,so for certain
applications, bandwidth is at premium, in which case there is a
definite need for speech coding at low bit rates, while maintaining
acceptable fidelity or quality of reproduction.
30. Draw the block diagram of compander? Mention the types of
companding?
Block Diagram
Types of companding:
1. µ law companding
2. A law companding
31. Define ADPCM.
It means adaptive differential pulse code modulation, a
combination of adaptive quantization and adaptive prediction. Adaptive
quantization refers to a quantizer that operates with a time varying step
size. The autocorrelation function and power spectral density of speech
signals are time varying functions of the respective variables. Predictors
for such input should be time varying. So adaptive predictors are used.
UNIT II
BASEBAND PULSE TRANSMISSION
1. What is an ISI in baseband binary system?
The transmitted signal will undergo dispersion and gets
broadened during its transmission through the channel. So they
happen to collide or overlap with the adjacent symbols in the
transmission. This overlapping is called Inter Symbol Interference.
2. What is correlative coding?
Correlative level coding is used to transmit a baseband
signal with a signaling rate of 2B0 over a channel of bandwidth
B0.This made physically possible by allowing ISI in the transmitted in
controlled manner. This ISI is known to the receiver. The correlative
coding is implemented by Duo binary signaling and modified Duo
binary signaling.
3. Define Duo binary baseband PAM system?
Duo binary encoding reduces the maximum frequency of the
baseband signal. The word means to double the transmission capacity
of the binary system. Let the PAM signal ak represents kth bit.Then
the encoder generates the new waveform as
Ck= ak+ak-1
Thus the two successive bits are added to get encoded value of kth bit.
Hence ck becomes a correlated signal even though ak is not correlated
.This introduces intersymbol interference in the controlled manner to
reduce the bandwidth.
4. What is the disadvantage of duo binary scheme?
The output if the duo binary encoder is given as
Ck= ak+ak-1
^
Let a represents an estimate of ak at the decoder. Then above equation
becomes
Ck= ak^+ak-1^
Hence ak^ can be obtained as
ak^= C k -ak-1^
This shows that if ck is received with error then ak will have error. This
error will propagate in the output sequence. This is the main drawback
of duo binary signaling.
5. What are eye patterns?
Eye pattern is used to study the effect of ISI in
baseband transmission.
i)Width of eye opening defines the interval overwhich the
received wave can be sampled without error from ISI.
ii) the sensitivity of the system to timing erroe is determined by
the rate of closure of the eye as the sampling time is varied.
iii) Height of the eye opening at sampling time is called margin over
noise.
6. How is the eye pattern obtained on the CRO?
Eye pattern can be obtained on the CRO by applying the
signal to one of the input channels and giving an external trigger of
1/Tb Hz. This makes one sweep of beam equal to Tb seconds.
7. What is the condition for zero inters symbol interference?
Zero ISI can be obtained if the transmitted pulse satisfies
the following condition
Time domain
p [(i-k)Tb]= 1
for i=k
0
for i≠k
Frequency domain
p [(i-k)Tb] =∑p(f-nfb)=Tb
8. How is the transfer function of matched filter related to the spectrum
of the input signal?
It is given as H(f) = (2k/N0)X*(f) e-j2πfT
Here X (f) is the spectrum of input signal.
9. From the eye pattern how is the best time for sampling determined?
It is preferable to sample the instant at which eye is open
widest. At this instant, the chances of error are minimum.
10. What is the purpose using an eye pattern?
Eye pattern can be used for
(i)
To determine an interval over which the received wave can
be sampled without error due to ISI.
(ii) To determine the sensitivity of the system to timing error.
(iii) The margin over the noise is determined from eye pattern.
11. Why do you need adaptive equalization in a switched telephone
network?
In a switched telephone network the distortion depends upon
(i)
Transmission characteristics of individual links
(ii)
Number of links in connection
Hence fixed pair of transmit and receive filters will not serve the
equalization problem. The transmission characteristics keep on changing.
Therefore adaptive equalization is used.
12. Discuss the merits and demerits of duo binary signaling?
Merits:
(i)
Higher signaling rate is allowed in reduced bandwidth
(ii) Effects of ISI are eliminated in the receiver
(iii) The performance is independent of signal being
transmitted.
Demerits:
(i)
Precoder is necessary to avoid error propagation
(ii) Sometimes additional bits of precoded sequence are
required in modified duo binary signaling.
13. What is meant by Nyquist channel?
The Nyquist channel is said to be ideal that produces zero ISI.
The ISI is zero if the pulse satisfies following criterion
∑P(f-nfb)=Tb
For the above condition to be satisfied, the spectrum of the pulse
must be of rectangular shape
P(f)=1/fb rect(f/fb)
This pulse is periodic in fb. Such pulse can be expressed in time domain
as
p(t) = sin(2πB0t)/ 2πB0t
Here B0 =fb/2 is called Nyquist bandwidth
Thus the transmitted signal will be succession of sinc pulses.If these
pulses are sampled at t=0,Tb,2Tb........ no ISI will be produced.
14. What are the merits and demerits of Nyquist channel?
Merits:
(i)
It eliminates an ISI completely
(ii) The method seems to be most easy
Demerits:
(i)
The transmission of exact sinc pulse is physically not
Possible.
15. What is meant by pseudo ternary signaling?
Successive 1’s are coded with alternate positive and negative
pulses. There are no pulses for zeros. Thus there are three voltage levels
+1,0 and -1.It can be NRZ as well as RZ type.
16. Why do we need equalization in baseband pulse transmission system?
When the signal is passed through the channel, distortion is
introduced in terms of (i) amplitude and (ii) delay. This distortion creates
the problem of ISI. The detection of the signal also becomes difficult.
This distortion can be compensated which the help of equalizers.
Equalizers are basically filters with correct the channel distortion.
17.A message has zero mean value and a peak value of 10V.It is to be
quantized using a step size of 0.1V with one level coinciding to 0V.Find
no. of bits required for encoding the quantized signal.
Step size (δ) = 2xmax/q
Here xmax is peak amplitude of the signal
0.1 =2x10/q
q = 200 levels
Number of bits (v) = loq2q = loq10q/log102 =log200/log2
= 7.643= 8
18. A TDM signal with bit time of 0.5 µs is to be transmitted using a
channel with raised cosine roll off factor of 0.5. What is the bandwidth
required?
Tb = 0.5 µs, α =0.5
B0 = fb/2 = 1/2Tb =1/(2x0.5x10-6) = 1x106
B = B0 (1+α)
=1x106(1+0.5)
=1.5 x106
19. Compare a baseband binary PAM system with that of M ary PAM
system
S.No Baseband binary PAM
M ary PAM
1.
There only two levels of
There are M levels of
representation. Thus there
amplitude of the waveform.
are only two symbols
Thus there are M symbols
2.
Symbol duration is Tb
Symbol duration is Tb log2M
3.
For every symbol
For every symbol transmitted
transmitted power is less
power is more and it varies
and remains constant
from symbol to symbol
4.
5.
6.
Detection of binary PAM is
simple,since there are only
two amplitude levels
Effect of noise is reduced
Transmission and receiving
circuit is simple
Detection of M ary PAM is
complex, since there are on
multiple amplitude levels
Effect of noise is more
compared to binary PAM.
Transmission and receiving
circuit is complex.
20 What is meant by forward and backward estimation?
AQF: Adaptive quantization with forward estimation. Unquantized
samples of the input signal are used to derive the forward estimates.
AQB: Adaptive quantization with backward estimation. Samples of
the quantizer output are used to derive the backward estimates.
APF: Adaptive prediction with forward estimation, in which
unquantized samples of the input signal are used to derive the forward
estimates of the predictor coefficients.
APB: Adaptive prediction with backward estimation, in which
Samples of the quantizer output and the prediction error are used to
derive estimates of the predictor coefficients.
21. What are the limitations of forward estimation with backward
estimation?
o Side information
o Buffering
o Delay
22. How are the predictor coefficients determined?
For the adaptation of the predictor coefficients the least mean
square (LMS) algorithm is used.
23. Define adaptive sub band coding?
It is a frequency domain coder, in which the speech signal is
divided in to number of subbands and each one is coded separately. It
uses non masking phenomenon in perception for a better speech quality.
The noise shaping is done by the adaptive bit assignment.
24. What are formant frequencies?
In the context of speech production the formant frequencies are the
resonant frequencies of the vocal tract tube. The formants depend on the
shape and dimensions of the vocal tract.
25.Define Adaptive filter?
It is a nonlinear estimator that provides an estimate of some desired
response without requiring knowledge of correlation functions, where the
filter coefficients are data dependent. A popular filtering algorithm is the
LMS algorithm.
26. Define modulation rate.
It is defined as the rate at which signal level is changed
depending On the nature of the format used to represent the digital data.It
is measured in Bauds or symbols per second.
27. State NRZ unipolar format
In this format binary 0 is represent by no pulse and binary 1 is
Represented by the positive pulse.
28. State NRZ polar format.
Binary 1 is represented by a positive pulse and binary 0 is
represented by a Negative pulse.
29. State NRZ bipolar format.
Binary 0 is represented by no pulse and binary one is represented
by the alternative positive and negative pulse.
38. State Manchester format.
Binary 0 : The first half bit duration negative pulse and the second half
Bit duration positive pulse.
Binary 1: first half bit duration positive pulse and the second half Bit
duration negative pulse.
30. What is the width of the eye?
It defines the time interval over which the received waveform can
be sampled without error from intersymbol interference.
31. What is sensitivity of an eye?
The sensitivity of the system to timing error is determined by the
rate of closure of the eye as the sampling time is varied.
32. What is margin over noise?
The height of the eye opening at a specified sampling time defines
the margin over noise.
UNIT III
PASS BAND DATA TRANSMISSION
1. Mention the need of optimum transmitting and receiving filter in
Baseband data transmission.
When binary data is transmitted over the base band channel,
noise interferes with it. Because of this noise interference, errors are
introduced in signal detection. Optimum filter performs two functions
while receiving the noisy signal:
i)
Optimum filter integrates the signal during the bit
interval and checks the output at the time instant
where signal to noise ratio is maximum.
ii)
Transfer function of the optimum filter is selected
so as to maximize signal to noise ratio.
iii) Optimum filter minimizes the probability of error.
iv)
2. Define ASK.
In ASK, carrier is switched on when binary 1 is to be
transmitted and it is switched off when the binary D is to be
transmitted ASK is also called on off keying.
3. What is meant by DPSK?
In DPSK, the input sequence is modified. Let input
sequence be d (t) output sequence be b(t). Sequence b (t) changes level
at the beginning of each interval in which d (t) =1 and it does not
change level when d (t)=0.
When b (t) changes level, phase of the carrier is changed.
And as stated above, b (t) changes its level only when d (t) = 1.This
means phase of the carrier is changed only if d(t)=1. Hence the
technique is called differential PSK.
4. Explain coherent detection.
In coherent detection, the local carrier generated at the
receiver is phase locked with the carrier at the transmitter. The
detection is done by correlating received noisy signal and locally
generated carrier. The coherent detection is a synchronous detection.
5. What is the difference between PSK and FSK?
In PSK, the phase of the carrier is switched according to
input bit sequence. In FSK, frequency of the carrier is switched
according to input bit sequence.FSK needs double the bandwidth of
PSK.
6. What is the major advantage of coherent PSK over coherent ASK?
ASK is on off signaling where as the modulated carrier
is continuously transmitted in PSK. Hence peak power requirement is
more in ASK whereas it is reduced in case of PSK.
7. What is meant by coherent ASK?
In coherent ASK, correlation receiver is used to detect
the signal. Locally generated carrier is correlated with incoming ASK
signal. The locally generated carrier is in exact phase with the
transmitted carrier. Coherent ASK is also called synchronous ASK.
8. Explain the model of band pass digital data transmission system?
The band pass digital data transmission system consists
of source, encoder and modulator in the transmitter. Similarly
receiver, decoder and destination form the transmitter.
9. What is base band signal receiver?
A base band signal receiver increases the signal to noise
ratio at the instant of sampling. This reduces the probability of error.
The base band signal receiver is also called optimum receiver.
10. What is matched filter?
The matched filter is a baseband signal receiver which
works in presence of white Gaussian noise. The impulse response of
the matched filter is matched to the shape of the input signal.
11. What is the impulse response of the matched filter?
Impulse response is given as
h(t) = 2k/N0 {x1(T-t)-x2(T-t)}
Here T is the period of sampling x1(t) and x2(t) are the two signals
used for transmission.
12. What is the value of maximum signal to noise ratio of the matched
filter? When it becomes maximum?
Maximum signal to noise ratio of the matched filter is the
ratio of energy of the signal to psd of white noise
Ρmax =E/(N0/2)
The maximum value occurs at the end of bit duration Tb.
13. On what factor, the error probability of matched filter depends?
Error probability of the matched filter is given as
Pe = ½ erfc √ (E/N0)
This equation shows that error probability depends only on energy
of the signal. It does not depend upon shape of the signal.
14. What is correlator?
Correlator is coherent receiver. It correlates the received
noisy signal f(t) with a locally generated replica of the known signal
x(t). Its output is given as
r(t) = ∫ f(t) x(t) dt
Matched filter and correlator are functionally same.
15. Which digital modulation technique gives better error probability?
Binary PSK gives reduced error probability compared to
ASK and FSK. It is given as
Pe = ½ erfc √ (E/N0)
16. Compare the probability of error of PSK with that of FSK.
S.NO
1.
2.
Error probability of PSK
Error probability of FSK
Pe = ½ erfc √ (E/N0)
For same E/N0 error
probability is less
Pe = ½ erfc √ (0.6 E/N0)
For same E/N0 error probability is
high.
17. Bring out the difference between carrier recovery and clock
recovery.
S.NO
1.
2.
Carrier recovery
Carrier is required for
coherent detection at the
receiver
Mth power loop, costas loop
are used for carrier recovery.
Clock recovery
Clock is required to
estimate correct bit timing
at the receiver.
Closed loop bit
synchronizer, early state
synchronizer are used for
clock recovery.
18. What are the advantages and disadvantages of DPSK?
Advantages:
i)DPSK does not need carrier at its receiver. Hence the
complicated circuitry for generation of local carrier is avoided.
ii)The bandwidth requirement of DPSK is reduced compared to
that of BPSK.
Disadvantages:
i)The probability of error or bit error rate of DPSK is higher than
that of BPSK.
ii) Since DPSK uses two successive bits for its reception error in
the first bit creates error in the second bit. Hence error
propagation in DPSK is more. Whereas in PSK single bit can go
in error since detection of each bit is independent.
19. Differentiate coherent and noncoherent receiver.
Coherent detection: In this method the local carrier generated at the
receiver is phase locked with the carrier at the transmitter. Hence it is also
called synchronous detection.
Noncoherent detection: In this method the receiver carrier need not be
phase locked with transmitted carrier. Hence it is also called envelope
detection. Noncoherent detection is simple but it has higher probability of
error.
20. What do you understand by continuous phase shift keying?
In FSK, when the phase change is gradual at the bit transition
times, the signal appears to be continuous in phase. This is called CPFSK.
To have phase continuity,the two FSK frequencies fH and fL must differ
by a bit rate of fb or 1/Tb.
21. Properties of matched filter.
The signal to noise ratio of the matched filter depends only upon
the the ratio of the signal energy to the psd of white noise at the filter
input
The output signal of a matched filter is proportional to a shifted
version of the auto_correlation function of the input signal to which the
filter is matched.
22. Why do we go for Gram-Schmidt Orthogonalization procedure?
Consider a message signal m. The task of transforming an
incoming message mi=1,2,…..M, into a modulated wave si(t) may be
divided into separate discrete time & continuous time operations. The
justification for this separation lies in the Gram-Schmidt
orthogonalization procedure which permits the representation of any set
of M energy signals, {si(t)}, as linear combinations of N orthonormal
basis functions, where N ≤M .
23. Explain how QPSK differs from PSK in term of transmission
bandwidth and bit information it carries?
For a given bit rate 1/Tb, a QPSK wave requires half the
transmission bandwidth of the corresponding binary PSK wave.
Equivalently for a given transmission bandwidth, a QPSK wave carries
twice as many bits of information as the corresponding binary PSK
24. Define Dibit.
A unique pair of bits is called a dibit. Gray encoded set of dibits
10, 00, 01 & 11
25. What are the three broad types of synchronization?
1. Carrier synchronization
2. Symbol & Bit synchronization
3. Frame synchronization.
26. What is carrier synchronization ?
The carrier synchronization is required in coherent detection
methods to generate a coherent reference at the receiver. In this
method the data bearing signal is modulated on the carrier in such
a way that the power spectrum of the modulated carrier signal
contains a discrete component at the carrier frequency.
27. What are the two methods for carrier synchronization?
1. Carrier synchronization using Mth Power loop
2. Costas loop for carrier synchronization
28. What is called symbol or bit synchronization?
In a matched filter or correlation receiver, the incoming
signal is sampled at the end of one bit or symbol duration.
Therefore the receiver has to know the instants of time at which a
symbol or bit is transmitted. That is the instants at which a
particular bit or symbol status and when it is ended. The
estimation of these times of bit or symbol is called symbol or bit
synchronization.
29. What are the two methods of bit and symbol synchronization?
1) Closed loop bit synchronization
2) Early late gate synchronizer
30. What are the disadvantages of closed loop bit synchronization?
1) If there is a long string of 1’s and o’s then y(t) has no
zero crossings and synchronization may be lost.
2) If zero crossing of y(t) are not placed at integer multiples
of Tb, the synchronization suffers from timing Jitter.
31. What is called frame synchronization ?
Depending on bits used for encoding, the word length is
defined. Thus each word container some fixed number of bits.
The receiver has to know when a particular frame status and when
its individual message bits status. This type of synchronization is
called frame synchronization.
32. Why synchronization is required ?
The signals from various sources are transmitted on the
single channel by multiplexing. This requires synchronization
between transmitter and receiver. Special synchronization bits are
added in the transmitted signal for the purpose. Synchronization is
also required for detectors to recover the digital data properly from
the modulated signal.
UNIT IV
ERROR CONTROL CODING
1. What is Hamming code distance?
The Hamming distance between the two code vectors is
equal to the number of elements in which they differ. For example let
the code words be
X = 101 and Y = 110
The two code words differ in second and third bits. Therefore the
hamming distance between X and Y is two.
2. Define code efficiency?
\
The code efficiency is the ratio of message bits in a block
to the transmitted bits for that block by the encoder
Code efficiency = message bits / transmitted bits =k/n
3. What is meant by systematic and nonsystematic codes?
In systematic block code, message bits appear first and
then check bits. In the nonsystematic code, message and check bits
cannot be identified in the code vector.
4. What is meant by linear code?
A code is linear if modulo-2 sum of any two code vectors
produces another code vector. This means any code vector can be
expressed as linear combination of other code vectors.
5. What are the error detection and correction capabilities of
Hamming c0odes?
The minimum distance of Hamming codes is 3. Hence
it can be used to detect double errors or correct single errors.
Hamming codes are basically linear block codes with dmin = 3.
6. What is meant by cyclic code?
Cyclic codes are the subclass of linear block codes.
They have the property that a cyclic shift of one code word produces
another code word
X = (xn-1, xn-2, …….x1, x0 )
Let us shift above code vector to left cyclically
X’ = ( xn-2, xn-3,…..x0,x1,xn-1 )
Above code vector is also a valid code vector.
7. How syndrome is calculated in Hamming codes and cyclic codes?
In Hamming code the syndrome is calculated as,
S = YHT
Here Y is the received and HT is the transpose of parity check matrix.
In cyclic code, the syndrome vector polynomial is given as
S(p) = rem [Y(p)/ G(p)]
Here Y(p) is the received vector polynomial and G(p) is the generator
polynomial.
8. What is BCH code?
BCH codes are most extensive and powerful error
correcting cyclic codes. The decoding of BCH codes is comparatively
simpler. For any positive integer m and t there exists a BCH code
with following parameters
Block length: n =2m-1
Number of parity check bits: n-k ≤ mt
Minimum distance: dmin ≥ 2t +1
9. What is RS code?
There are nonbinary BCH codes.The encoders for RS
codes operate on multiple bits simultaneously. The (n,k) RS code
takes the groups of m bit symbols of the incoming binary data stream.
It takes such k number of symbols in one block. Then the encoder
adds (n-k) redundant symbols to form the codeword of n symbols.
RS code has
Block length: n= 2m-1 symbols
Message size: k symbols
Parity check size: n-k = 2t symbols
Minimum distance: dmin = 2t +1 symbols
10. What is the difference between block codes and convolutional
Codes?
Block codes take k number of message bit
simultaneously and form n bit code vector. This code vector is also
called block. Convolutional code takes one message bit at a time and
generates two or more encoded bits. Thus convolutional codes
generate a string of encoded bits for input message string.
11. Define constraint length in convolutional codes.
Constraint strength is the number of shifts over which
the single message bit can influence the encoder output. It is expressed
in terms of message bits.
12. Define free distance and coding gain.
Free distance is the minimum distance between code
vectors. It is also equal to minimum weight of the code vectors.
Coding gain is used as a basis of comparison for
different coding methods. To achieve the same bit error rate coding
gain is defined as
A = [(E/N0) encoded]/ [(E/N0) coded]
For convolutional coding the coding gain is given as
A = rdf/2
Here r is the code rate
And df is the free distance.
13. What is convolutional code?
Fixed numbers of input bits are stored in the shift register
and they are combined with the help of mod 2 adders. This operation
is equivalent to binary convolution and hence it is called convolution
coding.
14. Define minimum distance.
It is the smallest hamming distance between the valid code
vectors. The error detecting and correcting capabilities of the codes
depend upon minimum distance.
15. List the advantages of Turbo codes.
i) They achieve the bit error probability of 10-5 using a rate ½ code
and E/N0 of 0.7 db of BPSK modulation over AWGN channel.
ii) It uses soft decision decoding compared to hard decision
decoding in convolutional codes.
iii) Turbo codes uses iterative algorithm for decoding the code
sequence.
iv) Turbo codes are constructed by using two or more component
codes on different interleaved versions of same information
sequence.
16. Give the special features of Trellis codes.
Trellis codes combine the modulation and coding in a single
entity. It has following features
i)
With Trellis coded modulation numbers of
signal points are larger for the same data rate.
This allows redundancy for forward error
correction without any increase in the
bandwidth.
ii)
iii)
With the help of convolutional coding there is
certain dependency between successive signal
points.Thus there are certain patterns or signal
points which is easier for detection.
The sequence structure is modeled as a trellis. It
uses soft decision decoding.
17. Define linear block code.
For the block of k message bits, (n-k) parity bits or check bits
are added. Hence the total bits at the output of channel encoder are n.
Such codes are called (n,k) block codes.
18. What are the fundamental properties exhibited by cyclic codes?
i) Linearity property: It states that the sum of any two code words is
also a valid code word. For example if X1 and X2 are two code words
X3 = X1 + X2
Here X3 is also a valid vector.
ii) Cyclic property : Every cyclic shift of a valid code vector produces
another valid code vector.
For example,
X = (xn-1, xn-2, …….x1, x0 )
Shifting the bits of above code vector to left cyclically by one bit
X’ = ( xn-2, xn-3,…..x0,x1,xn-1 )
Here X’ is also a valid code vector.
19. State any two properties of syndrome decoding.
1. The syndrome depends only on the error pattern and not on the
transmitted code word
2. All error patterns that differ by a code word have the same
syndrome.
20. What is meant by syndrome of linear block code?
The nonzero output of the produce YHT is called syndrome
and it is used to detect the errors in y. Syndrome is denoted by S and it
is given as
S = YHT
21. What is hamming distance?
The hamming distance between two code vectors is equal to the
number of elements in which they diffe r. For example let the two
code vectors be X=(101) and Y= (110) These two code vectors
differ in second and third bits. Therefore the hamming distance
between x and Y is two.
22. What is meant by systematic & non-systematic code?
In a systematic block code, message bit appear first and then check
bits. In the non-systematic code, message and check bits cannot be
identified in the code vector.
23. How syndrome is calculated in Hamming codes and cyclic codes?
In Hamming codes the syndrome is calculated as ,
S = YH T
Here Y is the received and H Tis the transpose of parity check
matrix. In cyclic code, the syndrome vector polynomial is given as,
S (P) = remainder ( y (p)/ G (P) )
Y(P) is received vector polynomial and G (p) is
generator polynomial.
24. What are the advantages of cyclic codes ?
1. Encoders and decoders for cyclic codes are simple
2. Cyclic codes also detect error burst that span many successive
bits.
UNIT V
SPREAD SPECTRUM MODULATION
1. Define pseudo-noise (PN) sequence.
A pseudo-noise sequence is defined as a coded sequence of 1s and
Os with certain autocorrelation properties. It is used in spread Spectrum
communications. It is periodic in that a sequence of 1s and 0s repeats
itself exactly with a known period.
2. What does the term catastrophic cyclic code represent ?
‘000’ is not a state of the shift register sequence in PN sequence
generator, since this results in a catastrophic cyclic code i.e once the 000
state is entered, the shift register sequence cannot leave this state.
3. Define a random binary sequence.
A random binary sequence is a sequence in which the presence of a
binary symbol 1 or 0 is equally probable.
4. State the balance property of random binary sequence.
In each period of a maximum length sequence, the number of 1s is
always one more than the number of 0s. This property is called the
balance property.
5. Mention about the run property.
Among the runs of 1s and 0s in each period of a maximum length
sequence, one half the runs of each kind are of length one, one fourth are
of length two, one eighth are of length three, and so or as long as these
function represent meaningful numbers of runs. This property is called
the run property.
6. Give the correlation property of random binary sequence.
The autocorrelation function of a maximum length sequence is
periodic and binary valued. This property is called the correlation
property.
7. Mention the significance of spread spectrum modulation.
An important attribute of spread-spectrum modulation is that it can
provide protection against externally generated interfering (jamming)
signals with finite power. The jamming signal may consist of a fairly
powerful broadband noise or multitone waveform that is directed at the
receiver for the purpose of disrupting communications. Protection
against jamming waveforms is provided by purposely making the
information bearing signal occupy a bandwidth far in excess of minimum
bandwidth necessary to transmit it.
8. What is called processing gain ?
Processing Gain (PG) is defined as the ratio of the bandwidth of
spread message signal to the bandwidth of unspreaded data signal ie).
9. What is called jamming effect ?
In the frequency band of the interest, somebody else transmits the
signals intentionally since these signals the in the frequency band of
transmission, they interface the required signal. Hence it becomes
difficult to detect the required signals. This is called jamming effect.
10. What is Anti jamming ?
With the help of spread spectrum method, the transmitted signals
are spread over the mid frequency band. Hence these signals appear as
noise. Then it becomes difficult for the jammers to send jamming
signals. This is called antijamming.
11. What are the three codes used for the anti jamming application ?
1. Golay code (24, 12)
2. Expurgated Golay (24, 11)
3. Maximum length shift register code.
12. What is called frequency hop spread spectrum ?
In frequency hop spread spectrum, the frequency of the carrier
hops randomly from one frequency to another frequency.
13. What is slow frequency hopping?
If the symbol rate of MFSK is an integer multiple of hop rate
(multiple symbols per hop) then it is called slow frequency hopping
14. What is fast frequency hopping?
If the hop rate is an integer multiple of symbol rate (multiple hops
per symbol) then it is called fast frequency hopping.
15. What are the two function of fast frequency hopping?
1. Spread Jammer over the entire measure of the spectrum of Txed
signal.
2. Retuning the Jamming signal over the frequency band of Txed
signal.
16.What are the features of code Division multiple Accesses?
1. It does not require external synchronization networks.
2. CDMA offers gradual degradation in performance when the no.
of users is increased But it is easy to add new user to the system.
3. If offers an external interference rejection capability.
17. What is called multipath Interference?
The interference caused by the interfacing of the signal form
the indirect path with the signal of direct path is called multipath
interference.
18. What is the advantage of a spread spectrum technique?
The main advantage of spread spectrum technique is its
ability to reject interference whether it be the unintentional
interference of another user simultaneously attempting to transmit
through the channel (or) the intentional interference of a hostile
transmitter to jam the transmission.
19. What is called frequency hop spread spectrum ?
In frequency hop spread spectrum, the frequency of the
carrier hops randomly from one frequency to another frequency.
20. What is slow frequency hopping?
If the symbol rate of MFSK is an integer multiple of hop rate
(multiple symbols per hop) then it is called slow frequency
hopping