Digital Communications ( 디지털 통신 )

1. Digital Communications(디지털 통신) 중앙대학교 전자전기공학부 이정우 Email: jwlee2@cau.ac.kr Homepage: http://cau.ac.kr/~jwlee2 office: 신공학관 409호 Phone: 820-5734

2. 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%), 참여도 (10%)

3. Introduction toDigital Communications

4. Open Systems Interconnection (OSI)Data Communication Model Covered in Digital Communications

5. Communication System Transmitter channel codeword message signal Source encoder source codeword Channel encoder Modulator Data waveform Channel Error control coding Compression received signal estimated message signal estimated source codeword estimated channel codeword Source decoder Channel decoder Demodulator User Receiver

6. 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

7. 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

8. 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.

9. 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.

10. 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 , whereεis the erasure probability.

11. Channel Capacity • Channel capacity of AWGN channel

12. 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.

13. 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.

14. 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.

15. 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

16. 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

17. Error Control Coding

18. +  +   Digital Communication Problem • Elements of digital communication system transmitter (phase shift keying modulation) message signal m(t) 0 → − 1 1 → + 1 for duration T channel output (received signal) x(t) transmitted signal s(t) channel carrier wave Accos(2πfc t), where fc=1/T noise w(t) decision making device say 1 if yT > 0 yT received signal x(t) say 0, otherwise correlator local carrier cos(2πfc t) receiver threshold=0

19. 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.

20. Topics inDigital Communications

21. Topics • Fourier Transform, Random Processes • Baseband Communications • signaling, matched filter, equalization, etc. • Passband Communications • signaling, coherent/noncoherent demodulation, Rayleigh and Rician distribution, etc. • Optimality • Maximum-likelihood (ML), maximum a posteriori (MAP) • Error Control Coding • Multiple Access Communications • Spread Spectrum Communications