Digital Communications

Digital communication System

Digital communication systems convert analogue signals into digital signals using Pulse Code Modulation (PCM)

PCM

involves sampling, quantization, and coding.

Sampling

• Sampling reads amplitude values of a continuous signal at regular intervals.

• The signal after sampling is a discrete time signal, also referred to as a PAM signal.

Impulse Signal

also known as ideal sampling.

Pulse Sampling

uses a train of pulses and can be natural or flat-top.

Natural Pulse

uses a FET as a switch.

Flat-top pulse sampling

uses a sample-and-hold circuit.

Sample and hold circuits

charge a capacitor during the sampling interval and hold the voltage for quantization.

Shannon's sampling theorem

states that an analogue signal with a max frequency of fmax can be reconstructed if the sampling frequency, fs, is greater than or equal to 2fmax.

fmax

fmax is the Nyquist frequency.

2fmax

Nyquist rate

Aliasing

when a signal is sampled below the Nyquist rate, causing a loss of information.

Quantization

converts the amplitude of a PAM signal into a discrete value.

Quantization width/resolution

is the spacing between quantization levels.

Non-uniform quantization

uses variable step sizes, achieved through compression and expansion (companding).

Mu-law and A-law

are companding standards.

Encoding

converts a quantised PAM signal into a code, usually binary.

The number of bits, n, required for a PCM code word is determined by n = log2(M), where M is the number of quantization levels.

Differential PCM (DPCM)

encodes the first sample and the differences between successive samples.

Delta modulation

compares consecutive quantized samples and outputs a 1 if the current is greater and a 0 if it is less than the previous one.

Slope overload

occurs if the input signal changes faster than the step generator in delta modulation.

Granular noise/hunting

is another error that can occur in delta modulation.

Line Coding

converts digital data to digital signals.

Desirable properties of a line code include no baseline wander, no DC components, self-synchronisation, built-in error detection, noise immunity, low complexity and transparency.

HDB3

Line code similar to AMI

Information Theory

Information theory provides a quantitative measure of information in message signals.

Discrete Information SourceA memoryless source produces symbols independent of previous symbols.

A discrete information source has a set of symbols as possible outcomes.

Memoryless source

A memoryless source produces symbols independent of previous symbols.

Information Content

The information content of a symbol is measured in bits.

Hartley Equation

The Hartley equation defines the information content of a symbol.

Entropy

Entropy is the average information content of a source.

Source Coding Theorem

The source coding theorem states that the minimum average length of a code word is related to the entropy.

Efficiency of a code

Efficiency of a code is the ratio of entropy to average length.

Binary Symmetric Source

A Binary Symmetric Source (BSS) has two outputs with probabilities z and (1-z).

Shannon-Hartley Theorem

Shannon-Hartley theorem defines the maximum data rate for a channel.

Source Coding

Source coding reduces the number of bits in a codeword.

Shannon-Fano // Huffman Coding

Shannon-Fano and Huffman coding are types of entropy coding.

Channel Coding

Channel coding detects and corrects errors in received data.

Random Errors

Random errors are single bit errors due to white noise.

Burst errors

Burst errors involve two or more bits in error due to a burst of noise.

Forward Error Correction (FEC)

Forward error correction (FEC) adds redundant bits for error correction.

Block Codes

Block codes add (n-k) redundant bits to k information bits.

Code rate

k/n

Redundant bits

(n-k)

Redundancy

[(n-k)/n] x 100%.

Hamming Distance

Hamming distance is the number of differing bits between two code words.

Minimum Hamming Distance

Minimum Hamming distance is the lowest Hamming distance in a code set.

Hamming Weight

Hamming weight is the number of ones in a codeword.

Systematic Codes

Systematic codes have separate data and redundant bits.

Linear Block Codes

Linear block codes have a modulo-2 sum of two codewords that is also a codeword.

Even Parity

Even parity adds a bit to make the total number of 1s even.

Odd Parity

Odd parity adds a bit to make the total number of 1s odd.

Cyclic Codes

Cyclic codes are a subset of linear block codes where a cyclic shift of a codeword results in another valid codeword.

CRC encoding

CRC encoding involves polynomial division to create a transmitted codeword.

Hamming Codes

Hamming codes are used for single-error correction.

Check bits at the receiver

determine the location of an error.

Hamming Codes: Parity bits

Parity bits are placed at bit positions that are powers of 2 (e.g., 1, 2, 4, 8).

Parity bits are calculated based on the data bits.

Digital Modulation

Digital modulation uses digital messages to modulate a high-frequency carrier wave.

Amplitude Shift Keying (ASK)

• Amplitude Shift Keying (ASK) changes the amplitude of the carrier.

  • On-Off Keying (OOK) is a variant of ASK.

Frequency Shift Keying (FSK)

• Frequency Shift Keying (FSK) changes the frequency of the carrier.

  • Continuous Phase FSK (CPFSK) has smooth transitions.

Phase Shift Keying (PSK)

• Phase Shift Keying (PSK) changes the phase of the carrier.

  • Binary PSK (BPSK) uses two phases.

  • Quadrature PSK (QPSK) uses four phases.

Differential PSD (DPSK)

Differential PSK (DPSK) encodes data based on phase changes relative to the previous bit.

Noise

Noise is unwanted voltages and currents that corrupt the signal.

External Noise

External noise includes man-made, atmospheric, and space noise.

Internal Noise

Internal noise includes thermal, shot, and flicker noise.

Thermal Noise

Thermal noise is due to the thermal agitation of electrons.

Noise Power

Power available to the load

Noise Power

Noise power is the power available to the load.

Spectral Noise Power Density

Power per unit frequency

Additive White Gaussian Noise (AWGN)

Additive White Gaussian Noise (AWGN) is thermal noise with a white spectrum and Gaussian distribution.

Signal-to-noise ratio (SNR)

Signal-to-noise ratio (SNR) compares signal power to noise power.

Noise Ration (NR)

Noise ratio (NR) is the ratio of input to output SNRs.

Noise Figure (NF)

10log(NR)

Intermodulation Noise

Intermodulation noise occurs due to non-linearities in the communication channel.

Optical Communication Systems

Optical communication systems use light to transmit information.

Transmitters

Transmitters use LEDs or lasers.

Excitation

Excitation is when an electron moves to a higher energy level.

Emission

Emission occurs when an electron returns to a lower energy level.

Spontaneous Emission

Spontaneous emission occurs naturally.

Stimulated Emission

Stimulated emission is induced by a passing photon.

LED

• LEDs are pn-junction semiconductor devices that emit light when forward biased.

  • They can have a homojunction or heterojunction structure.

  • They can be surface or edge emitters.

LASER

• LASERs use stimulated emission of radiation for light amplification.

  • They require population inversion for lasing action.

  • Laser light is monochromatic, coherent, has a narrow beam, and high irradiance.

Output Power

Output power is the optical power emitted.

Output Pattern

Output pattern is the area and angle of emitted light.

Spectral Width

Spectral width is the range of wavelengths emitted.

Modulation

can be direct or indirect:

Direct modulation

Direct modulation varies the electrical supply to the light source.

Indirect Modulation

Indirect modulation uses an external modulator.

Responsivity

Responsivity is the ratio of electrical power output to optical power input.

Quantum efficiency

Quantum efficiency is the ratio of electrons generated to incident photons.

Dark current

Dark current is the current generated with no light.

Noise Floor

Noise floor is the minimum detectable power.

Response Time

Response time is the time to respond to an optical input.

Noise equivalent power (NEP)

Noise equivalent power (NEP) is the power for a signal-to-noise ratio of one.

Optical Fibres

Optical fibres consist of a core, cladding, and jacket.

Refractive index

Refractive index determines the velocity of light in a material.

Reflection

Reflection occurs at the boundary of two media.

Refraction

Refraction is the bending of light at a boundary.

Snell’s Law

Snell's law relates the angles and refractive indices of two media.

Critical Angle

Critical angle is the angle of incidence where the angle of refraction is 90 degrees.

Cone of acceptance

The cone of acceptance defines the rays that can propagate through a fibre.