Digital Communications( 디지털 통신 )

중앙대학교 전자전기공학부이정우

Email: jwlee2@cau.ac.krHomepage: http://cau.ac.kr/~jwlee2

office: 신공학관 409 호Phone: 820-5734

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• 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 4 번 ( 각 5%), 참여도 (10%)

Introduction toDigital Communications

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Open Systems Interconnection (OSI)Data Communication Model

Covered in Digital Communications

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Communication System

Channelencoder

Sourceencoder

Modulator

Demodulator

Channel

Channeldecoder

Sourcedecoder

Error controlcoding

Compression

Transmitter

Receiver

waveform

received signal

channelcodeword

estimatedchannel

codeword

sourcecodeword

estimatedsource

codeword

messagesignal

estimatedmessage

signal

Data

User

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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

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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

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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 error-

free 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 e

ntropy with the parameter ρ.

• BEC

C = 1 – ε ,where ε is the erasure probability.

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Channel Capacity

• Channel capacity of AWGN channel

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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), pulse-position modulation (PPM)

• Other names: frequency shift keying (FSK), amplitude-shift 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

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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

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Error Control Coding

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Digital Communication Problem

• Elements of digital communication system

messagesignal m(t)0 → − 11 → + 1for duration T

transmittedsignal s(t)

carrier waveAccos(2πfc t), where fc=1/T

noise w(t)

channel output(received signal) x(t)

+

+

T

dt0

decisionmakingdevice

say 1 if yT > 0

say 0, otherwise

threshold=0local carriercos(2πfc t)

receivedsignal x(t)

transmitter(phase shift keying modulation)

channel

receiver

yT

correlator

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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.

Topics inDigital Communications

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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