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 Test “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%)

Introduction to Digital Communications

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

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

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

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

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.

Channel Capacity Shannon (1948) Definition of channel capacity C 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.

Channel Capacity AWGN channel C = W log2 (1 + SNR) bit/sec, BSC 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.

Channel Capacity Channel capacity of AWGN channel

Modulation Modulation: Demodulation: 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.

Modulation Continuous wave (CW) modulation Pulse 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.

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.

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

Error Control Coding Classification Block codes Tree 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

Error Control Coding

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) yT decision making device say 1 if yT > 0 received signal x(t)  say 0, otherwise correlator local carrier cos(2πfc t) receiver threshold=0

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 in Digital Communications

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