Digital Communications
(디지털 통신)
중앙대학교 전자전기공학부
이정우
Email: jwlee2@cau.ac.kr
Homepage: http://cau.ac.kr/~jwlee2
office: 신공학관 409호
Phone: 820-5734
• Main text: class notes
• References
– “Digital transmission of information” by Richard E. Blahut,
Addison-Wesley, 1990.
– “Communication systems” by Simon Haykin, John Wiley &
Sons, 2001.
• Test
– 중간고사 (35%), 기말고사 (35%), 과제물 4번 (각 5%), 참여
도 (10%)
2
Introduction to
Digital Communications
Open Systems Interconnection (OSI)
Data Communication Model
Covered in Digital Communications
4
Communication System
Transmitter
message
signal
source
Source
encoder codeword
Channel
encoder
channel
codeword
Modulator
waveform
Data
Compression
Error control
coding
Channel
received signal
estimated
message
signal
User
estimated
source
Source
decoder codeword
Channel
decoder
estimated
channel
codeword
Demodulator
Receiver
5
Communication System
• Two basic modes of communications
– Broadcasting
• Single powerful transmitter and many receivers
• TV, Radio, etc.
– Point-to-point communication
• Link between a single transmitter and a receiver
• Telephone
6
Communication Resources
• Two primary resources
– Transmitted power
• Average power of transmitted signal
– Channel bandwidth
• Band of frequencies allocated for transmission
• System design objective
– Use two resources as efficiently as possible.
– Power limited vs. Band limited
7
Communication Channels
• Guided propagation vs. free propagation
– telephone channels, coaxial cables, optical fibers, etc.
– broadcast channels, mobile radio channels, satellite
channels, etc.
• Random error vs. burst error
– Deep-space channels, satellite channels
– Radio channels, wire and cable, magnetic recording
channel, etc.
• Discrete vs. continuous
– Binary symmetric channel (BSC), binary erasure channel
(BEC)
– Additive white Gaussian noise (AWGN) channel, Fading
channels (Rayleigh, Rician), etc.
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Channel Capacity
• Shannon (1948)
– If you transmit information at a rate R < C, then the errorfree transmission is possible.
• Definition of channel capacity C
– Maximum rate at which information can be transmitted
across the channel without error.
• Goal of communication system design in power-limited
environment:
– achieve a target error rate of data transmission with as low
signal power as possible.
• Similar to achieving the capacity bound as close as possible
with less power.
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Channel Capacity
•
AWGN channel
C = W log2 (1 + SNR) bit/sec,
where W denotes the channel bandwidth and SNR denotes the
signal to noise ratio.
•
BSC
C = 1 – H(ρ) ,
where ρ is the error probability of the channel and H(ρ ) is the
entropy with the parameter ρ.
•
BEC
C=1–ε,
where ε is the erasure probability.
10
Channel Capacity
• Channel capacity of AWGN channel
11
Modulation
• Modulation:
– Modifies the message signal into a form suitable for
transmission over the channel.
• Demodulation:
– Recreates the original message signal from a degraded
version of the transmitted signal after propagation through
the channel.
– Due to the presence of noise, the original message signal
cannot be recreated exactly.
– The degradation is influenced by the type of modulation
scheme.
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Modulation
• Continuous wave (CW) modulation
– Carrier is a sinusoidal wave.
– Amplitude modulation (AM), frequency modulation (FM),
phase modulation (PM)
• Pulse modulation
– Carrier is a periodic sequence of rectangular pulses.
– Pulse-amplitude modulation (PAM) or amplitude-shift
keying (ASK), pulse-duration modulation (PDM), pulseposition modulation (PPM)
• Other names: frequency shift keying (FSK), amplitudeshift keying (ASK), on-off keying (OOK), phase-shift
keying (PSK), M-ary orthogonal keying, etc.
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Modulation
• Another benefit: Multiplexing
– Combines several message signals for their simultaneous
transmission over the same channel.
• Frequency-division multiplexing (FDM)
– CW modulation is used.
– Assigns message signal distinct carrier frequency.
• Time-division multiplexing (TDM)
– Pulse modulation is used.
– Different time slots
• Code-division multiplexing (CDM)
– Each message is identified by a distinctive code.
– Message signals are permitted to overlap in both time and
frequency.
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Error Control Coding
• Channel encoder produces a new sequence of symbols
called the channel codeword.
• Controlled redundancy exists in the construction of
channel codeword.
– Channel codeword is longer than source codeword.
• Benefits
– In principle:
• If you transmit information at a rate R < C, then the error-free
transmission is possible.
– In practice:
• Reduce the error rates
• Reduce the transmitted power requirements
15
Error Control Coding
• Classification
– Block codes
• Hamming, BCH, RS, Golay, Goppa, Algebraic geometric
codes (AGC), LDPC codes
Tree codes
• Convolutional codes, turbo codes
– Linear codes
• Hamming, BCH, RS, Golay, Goppa, AGC, LDPC, turbo, etc.
Nonlinear codes
• Nordstrom-Robinson, Kerdock, Preparata, etc.
– Systematic codes vs. Nonsystematic codes
16
Error Control Coding
17
Digital Communication Problem
• Elements of digital communication system
transmitter
(phase shift keying modulation)
message

signal m(t)
0→−1
1→+ 1
for duration T carrier wave
Accos(2πfc t),
where fc=1/T
received
signal x(t)

transmitted
signal s(t)
+ 
+
channel output
(received signal) x(t)
channel
noise w(t)

T
0
dt
yT
decision
making
device
say 1 if yT > 0
say 0, otherwise
correlator
local carrier
cos(2πfc t)
receiver
threshold=0
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Digital Communication Problem
• Theoretical issues
– Justification of the receiver structure.
– Finding a random variable describing the noise.
– Determining the probability of decision of errors.
• Practical issues
– Choice of modulation scheme conserving bandwidth in a
cost-effective manner.
– Design of channel encoder/decoder to be close to the
channel capacity.
– Synchronization of the carrier frequencies in modulator
and demodulator.
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Topics in
Digital Communications
Topics
1. Fourier Transform, Random Processes
2. Baseband Communications
•
signaling, matched filter, equalization, etc.
3. Passband Communications
•
signaling, coherent/noncoherent demodulation, Rayleigh
and Rician distribution, etc.
4. Optimality
•
Maximum-likelihood (ML), maximum a posteriori (MAP)
5. Error Control Coding
6. Multiple Access Communications
7. Spread Spectrum Communications
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