Week 3 lectures
Communication system block diagram (from Proakis
and Salehi, page 8)
Source coding: Digital representation of information:
block-oriented, stream-oriented (Section 3.1)
Text: ASCII (7bits for each character) and EBCDIC;
extended ASCII uses 8 bits per character
Compression techniques: "the" "e" occur a lot
Fax of an 8" by 10" page with 400 by 400 pixels
per sq. inch results in 38.4Mbytes if three bytes are used, one each to
represent R, G, and B.
GIF: lossless compression
JPEG: lossy compression
Voice: PCM (Pulse Code Modulation); 8000 samples/sec;
with 8 bits/sample, it results in 64Kbps.
ADPCM - 32 Kbps
Residual excited linear predictive coding - 8-16
Audio (music): needs 32-384Kbps
H.261 coding: 176 by 144 or 352 by 258 frames
at 10-30 frame/sec
Full motion MPEG-2
HDTV - 1920 by 1080 frames at 30 frames/sec (aspect
ratio is important 16:9 vs. 4:3)
Requirements of different traffic types:
Audio: sensitive to delay and jitter (delay variation)
Transmission (emission) delay is L/R where L bits
needs to be transferred over a channel operating at R bits/sec
Propagation delay is distance divided by speed
of light in medium of the channel
Packetization delay: time to create an audio
packet to send on a packet-switched network or to create a voice sample
to send on a circuit-switched network; depends on the codec rate; for example,
G.711 codecs operate at 64Kbps
For telephony traffic, the one-way delay should
Less than 25ms for excellent quality voice without
Less than 150ms for excellent quality voice with
Less than 400ms for acceptable quality voice with
Text/data: sensitive to loss
Channel related aspects: Why digital communications?
Advantages of digital communication over analog
Analog communication: all details must be reproduced
vs. digital communication: only a discrete set of levels need to be reproduced
Analog repeaters vs. Digital repeaters
Analog repeaters: Amplifier and equalizer; the
amplifier amplifies both the signal and noise. High frequencies attenuate
more than low frequencies; also delays are frequency-dependent. The equalizer
removes these differences. The signal on the output of the repeater has
noise and signal components.
Digital repeaters: Amplifier/equalizer; output
is fed into a timing recovery circuit and a decision circuit and signal
regenerator; the output signal is regenerated to a string of 1s and 0s.
There can still be errors, i.e., a 1 can appear as a 0 or vice versa, but
there is no degradation as in the analog case. This makes digital communications
cheaper, because transmission can be achieved to longer distances at the
same power, or at the same distance with lower power.
Basic properties of digital transmission systems
Concept of "Bandwidth of a channel:" The bandwidth
W of a channel is the range of frequencies that is passed by the channel.
The amplitude response function of a low pass channel is such that past
W, the ampliture drops off to zero - see Fig. 11 of your textbook.
Nyquist rate: The fastest rate at which pulses
can be transmitted into a channel of bandwidth W is given by the Nyquist
rate, which is 2W pulses/sec. It is also the minimum rate at which a signal
of maximum bandwidth W needs to be sampled.
In case of multi-level transmission, where there
are m bits/pulse, which corresponds to M=2m levels, the Nyquist
rate is 2Wm bits/sec. This seems to indicate that by increasing the number
of levels, the rate at which pulses are sent on a channel can be arbitrarily
increased. This is not true because as the number of levels increases,
it becomes harder to detect levels accurately; this leads to higher noise
Concept of "Signal to Noise Ratio:" It is the
ratio of the average signal power to the average noise power. SNR (dB)
= 10 log10 SNR; SNR is typically expressed in decibels (dB).
Shannon's channel capacity: The maximum rate at
which bits can be transferred reliably.
Example, if SNR expressed in dB is 20dB, it means
that SNR is 100; To find log2 x, find (log10x)/log102.
C=W log2(1+SNR) bits/sec when W
is expressed in hertz.
SNR is the signal to noise ratio at the receiver
If 2y = 101, take log10
of both sides, then y log102 = log10101.
The maximum rate at which a signal can be transferred
reliably depends upon four factors:
The Shannon's formula reflects these four factors.
Distance impacts attentuation, which in turn, affects received signal strength.
energy of signal
bandwidth of the channel
Line (channel) coding (Section 3.6): is a method for converting a binary
information sequence (1s and 0s) into a digital signal in a digital communications
reduce DC or low frequencies because some media do not all these to
pass, e.g., telephone systems do not transmit <200Hz.
extract timing information
built-in error detecting capabilities giving the signal better immunity
to noise and interference
Line coding methods:
Unipolar NRZ: +A voltage for 1; 0 voltage for 0.
Polar NRZ: +A/2 for 1; -A/2 for 0
Bipolar: 0: mapped to 0 voltage; alternate 1s mapped to +A/2 and -A/2.
Manchester coding: a RZ coding scheme; 1: transition from +A/2 to -A/2;
0: transition from -A/2 to A/2 within the bit time.
Low frequencies: See Fig. 3.36 in textbook - spectra for different
line codes. A signal consists of one or more frequencies. Both the unipolar
NRZ and polar NRZ have the same frequency components because they have
the same variations in the signal as a function of time. Both have low
frequencies because a string of consecutive 1s or a string of consecutive
0s is possible. In contrast, bipolar coding does not have low frequencies.
Because a string of 1s will generate a square wave with frequency 1/2T
Hz, where 2T is the period of the square wave. But what about a string
of 0s? Whenever a string of 0s occurs, the string is encoded into a special
binary sequence that contains 0s and 1s. To notify the receiver that
such a mapping has been done, the sequence is encoded so that the usual
rule of changing the voltage level from +A/2 to -A/2 for alternate 1s is
violated, that is two consecutives 1 do not alternate in polarity.
Timing extraction: RZ codes are better for this since midway through
the bit time, RZ will return to zero. Frequency of RZ signals are twice
as much as NRZ; hence RZ coding is not good for bandwidth limited channels.
But it makes clock recovery easier. RZ: A 1 is represented as a transition
as is a 0. Low frequency content is small.
Bandwidth efficiency: Bipolar coding is useful in long-distance transmission
where bandwidth is limited, while Manchester coding, which requires more
bandwidth but has simple timing recovery is used in LANs. See Spectra of
line codes to notice that the frequency range of Manchester coding is much
more than bipolar.
Error detecting capabilities: The Manchester encoding can be seen as
the transmission of two pulses for each binary bit. A binary 1 is mapped
to 10 and a binary 0 is mapped to 01, and the corresponding polar encoding
of these two bits is transmitted. The Manchester code is an example of
a mBnB code, wher m is 1 and n is 2. In general m information bits are
mapped to n >m encoded bits. FDDI uses 4B5B line coding.
GbE uses 8B10B. With optical transmission, negative voltage is not
possible, light pulse is sent for a 1 and nothing for a 0. So with
an optical version of the Manchester coding, uses unipolar coding instead
of polar after the mapping of 1 to 10 and 0 to 01.
Examples used in existing networks:
Telephone transmission systems: bipolar coding
Modulation (Section 3.7 - upto and including 3.7.1; QAM not included)
If a channel is not low pass, it may pass a set of frequencies [f1,
f2] centered around some frequency fc. The bandwidth
of such a channel is f2-f1.
To transmit a signal on such a channel, the signal needs to be modulated
on to a carrier frequency fc.
Three forms of modulation: ASK (Amplitude Shift Keying), FSK (Frequency
Shift Keying), PSK (Phase Shift Keying).
Consider a PSK signal:
If the information bit is 1, +ACos(2pfct)
If the information bit is 0, -ACos(2pfct)
The baseband signal, a digital string of 1s and 0s is denoted Ak.The
modulated signal is
Ak Cos (2pfct)
To demodulate, multiply by 2 Cos (2pfct)
and then send through a low-pass filter.
The reason this works is that Ak Cos (2pfct)
x 2 Cos (2pfct) = Ak
The second component will not be passed through the filter and the string
of 1s and 0s is output. The filter is a low pass filter of band W. The
baseband signal Ak is of bandwidth W, which is the range of
frequencies around fc that the medium can carry. The second
term is another band of +/- W around 2fc. This will be filtered
out by the low pass filter.