Encoding and Modulation

Encoding and Modulation

In digital communication, a digital signal has to be turned into a signal that can travel over a channel. Encoding and modulation are the two techniques that make this possible.

1. Encoding Techniques

Encoding converts a digital signal into a signal form suited to transmission. Its main purpose is to improve the reliability and the efficiency of the transmission.

1.1 Non-Return-to-Zero Encoding (NRZ)

Characteristics:

• A high level represents 1, a low level represents 0
• The signal does not return to zero during the bit period
• Simple and direct, but it has synchronisation problems

Advantages and disadvantages:

• Advantage: simple to implement, high bandwidth utilisation
• Disadvantage: it has a DC component, which makes synchronisation difficult

1.2 Manchester Encoding

Characteristics:

• There is one transition in the middle of every bit period
• A high-to-low transition represents 1, a low-to-high transition represents 0
• Or the other way round, depending on the standard

Encoding rules:

Advantages:

• It carries its own clock information, so synchronisation is easy
• No DC component
• Strong resistance to interference

Disadvantages:

• Lower bandwidth utilisation (it needs twice the bandwidth)
• The coding efficiency is 50%

1.3 Differential Manchester Encoding

Characteristics:

• A transition at the start of a bit period means 0, no transition means 1
• Or the other way round, depending on the standard
• It is more resistant to interference than Manchester encoding

Encoding rules:

1.4 4B/5B Encoding

Characteristics:

• Four data bits are encoded into five transmitted bits
• It guarantees that the transmitted code never contains more than three consecutive zeros
• It improves the reliability of the transmission

Encoding table:

2. Modulation Techniques

Modulation converts a digital signal into an analog signal so that the digital signal can travel over an analog channel.

2.1 Amplitude Shift Keying (ASK)

Principle:

• Carriers of different amplitudes represent different digital signals
• Two amplitudes are usually used: a high amplitude for 1 and a low amplitude for 0

Mathematical expression: $s(t) = A \cos(2\pi f_c t)$

where $A$ takes its value from the digital signal.

Characteristics:

• Simple to implement
• Weak resistance to noise
• Suitable for low-speed transmission

2.2 Frequency Shift Keying (FSK)

Principle:

• Carriers of different frequencies represent different digital signals
• Two frequencies are usually used: $f_1$ for 1 and $f_2$ for 0

Mathematical expression: $s(t) = A \cos(2\pi f_i t)$

where $f_i$ is $f_1$ or $f_2$, chosen according to the digital signal.

Characteristics:

• Strong resistance to noise
• Relatively simple to implement
• Low bandwidth utilisation

2.3 Phase Shift Keying (PSK)

Principle:

• Carriers of different phases represent different digital signals
• The most common variant is BPSK (binary phase shift keying)

BPSK (binary phase shift keying):

• A phase of 0 degrees represents 0, a phase of 180 degrees represents 1

Mathematical expression: $s(t) = A \cos(2\pi f_c t + \phi)$

where $\phi$ takes the value 0 or $\pi$ according to the digital signal.

QPSK (quadrature phase shift keying):

• Four distinct phases carry 2 bits of data
• The phases are spaced 90 degrees apart

Characteristics:

• Strong resistance to noise
• High bandwidth utilisation
• Relatively complex to implement

2.4 Quadrature Amplitude Modulation (QAM)

Principle:

• The amplitude and the phase of the carrier are modulated at the same time
• Several bits can be transmitted in one symbol

A 16QAM example:

• 16 distinct amplitude-phase combinations are used
• Each symbol transmits 4 bits of data

Characteristics:

• Very high bandwidth utilisation
• Fairly strong resistance to noise
• Complex to implement

3. Choosing Between Encoding and Modulation

3.1 Factors to Consider

1. Required transmission rate

   • High-speed transmission: choose QAM or QPSK
   • Low-speed transmission: choose ASK or FSK

2. Channel characteristics

   • Noisy: choose PSK or QAM
   • Bandwidth limited: choose QAM or QPSK

3. Implementation complexity

   • Simple implementation: choose ASK or FSK
   • Complex implementation: choose QAM

4. Cost

   • Low cost: choose ASK or FSK
   • High performance: choose QAM or QPSK

3.2 Common Applications

Wired communication:

• Ethernet: Manchester encoding
• Optical fibre: NRZ encoding
• Cable: 4B/5B encoding

Wireless communication:

• WiFi: OFDM + QAM
• Mobile communication: QPSK, QAM
• Bluetooth: GFSK

4. Modern Encoding Techniques

4.1 Error-Correcting Codes

Forward Error Correction (FEC):

• Redundant information is added to the data
• The receiver can detect and correct errors
• Examples: Hamming codes, BCH codes, Reed-Solomon codes

4.2 Compression Codes

Data compression:

• Reduces the amount of data to be transmitted
• Improves transmission efficiency
• Examples: Huffman coding, arithmetic coding

4.3 Adaptive Coding

Adaptive Modulation and Coding (AMC):

• The encoding and modulation scheme is adjusted dynamically to the channel quality
• Higher-order modulation is used when the channel quality is good
• Lower-order modulation is used when the channel quality is poor

5. Performance Metrics for Encoding and Modulation

5.1 Bit Error Rate (BER)

Definition: the ratio of the bits received in error to the total number of bits

Factors:

• Signal-to-noise ratio
• Modulation scheme
• Encoding scheme

5.2 Spectral Efficiency

Definition: the data transmission rate within a unit of bandwidth

Unit: bps/Hz

How to improve it:

• Use higher-order modulation
• Adopt efficient encoding
• Optimise the signal design

5.3 Power Efficiency

Definition: the power required to transmit one bit

How to improve it:

• Use error-correcting codes
• Optimise the modulation scheme
• Adopt power control