Modulation Schemes & Decoding | Communication System - Electronics and Communication Engineering (ECE) PDF Download

Introduction

The term digital communication covers a broad set of techniques used to convey information in digital form. Two principal interpretations are commonly used: one is digital transmission, which refers to the transmission of digital pulses between two or more points in a communication system; the other is digital radio, which refers to the transmission of digitally modulated analog carriers between two or more points.

• Regeneration is a primary advantage of digital signals: a digital waveform can be restored to its original shape at intervals, reducing cumulative distortion over long links.
• The waveform at the receiver is affected by two main mechanisms:
  • non-ideal transfer functions of transmission lines and circuits, which distort the ideal pulse shape;
  • unwanted electrical noise or interference that further alters the pulse waveform.
• As the pulse shape degrades with distance, circuits that identify and restore the transmitted pulse are used periodically; these circuits are called regenerative repeaters.
• Additional advantages of digital circuits are:
  • less sensitivity to distortion and interference compared with analog circuits;
  • greater reliability and often lower manufacturing cost;
  • natural suitability for digital signal processing techniques that protect against interference and jamming.

Elements of Digital Communication

• The source may produce an analog signal (for example, voice or video) or a digital signal (for example, a teleprinter output) that is discrete in time and has a finite alphabet of symbols.
• Source encoding (or data compression) converts the source output into a sequence of binary digits efficiently so that redundancy at the source is reduced while essential information is preserved.
• Channel encoding adds controlled redundancy to the binary information sequence so that the receiver can detect and correct errors introduced by channel noise and interference; this improves the reliability and fidelity of received data.
• The digital modulator maps the binary information sequence into signal waveforms suitable for transmission over the physical channel, since practically all channels transmit waveforms.
• For a channel bit rate of R bits per second, a binary modulation maps each bit into a waveform s0(t) or s1(t) and transmits one bit at a time. This is called binary modulation.
• Alternatively, an M-ary modulation maps b coded bits at a time into one of M = 2^b distinct waveforms s_i(t), i = 0,1,...,M-1. A new b-bit block enters the modulator every b/R seconds; thus each M-ary waveform occupies b times the time of a single binary symbol when the overall channel bit rate R is fixed.
• At the receiver, the digital demodulator processes the channel-corrupted waveform and produces a sequence of numbers that are estimates of the transmitted data symbols (binary or M-ary).
• The channel decoder reconstructs the original information sequence using knowledge of the channel code and any redundancy present in the received data.
• The source decoder then attempts to reconstruct the original source signal from the output of the channel decoder, using knowledge of the source encoding method.

Pulse Code Modulation (PCM)

• Pulse Code Modulation (PCM) is a fundamental pulse digital modulation scheme in which each analogue sample value is quantized and represented by a digital codeword.
• PCM operation comprises sampling an analogue signal, quantizing each sample to a discrete amplitude level, encoding the quantized level into binary form, and transmitting the resulting digital codes.
• If an n-bit quantizer is used and the sampling rate is f_s, the resulting bit rate is R_b = n · f_s bits per second.

• At the receiver, essential operations include regeneration of impaired signals, decoding of the channel code and demodulation of the stream of quantized samples.
• Typical bandwidth requirements for baseband PCM depend on pulse shape: a useful rule of thumb gives a minimum approximate bandwidth of R_b/2 and a maximum of R_b, depending on signalling and filtering used.

Quantization

Quantization replaces a continuously varying sample amplitude by the nearest value from a finite set of amplitude levels. Quantization therefore introduces an error called the quantization error.

• Quantizers are broadly of two types:
  • Uniform quantizer;
  • Non-uniform quantizer.

Uniform Quantizer

• In a uniform quantizer the quantization step size remains the same across the entire input range.
• Assume the signal amplitude m(t) is confined to the range (-m_p, +m_p). This total range 2m_p is divided into L levels, each of step size δ = 2 m_p / L.
• A sample amplitude is approximated by the midpoint of the interval in which it lies; common implementations are the mid-tread and mid-rise types of uniform quantizer.

• The maximum quantization error (for a uniform quantizer) is ±Δ/2, where Δ denotes the step size.

Non-uniform Quantizer

• In a non-uniform quantizer the step size varies with the input amplitude; smaller steps are used where the signal is more likely to occur and larger steps where it is less likely.
• Non-uniform quantization reduces the audible or perceptual effect of quantization error for typical signals such as speech.
• For PCM with a sinusoidal input, the signal-to-quantization-noise ratio (SQNR) for a uniform quantizer is given by the expression shown below.

In the expression above, n is the number of bits in the quantizer.

• Increasing the number of quantizer bits improves SQNR, but increases the bit rate R_b and therefore the bandwidth required for transmission.

Companding Process

Companding combines compression at the transmitter and expansion at the receiver. Compression and expansion are implemented by passing the signal through amplifiers having non-linear transfer characteristics chosen so that small amplitudes are amplified relative to large amplitudes prior to quantization; at the receiver the inverse law is applied to restore the dynamic range.

Companding reduces the effective quantization noise for small-amplitude signals and is widely used in telephony to reduce audible distortion and to compensate for level differences between different talkers.

• Two common companding laws are μ-law and A-law.

μ-law Companding

• μ-law uses a continuous logarithmic compression characteristic; it makes quantization intervals approximately proportional to the input level so that quantization noise scales with signal level.
• The parameter from the source material is given as μ_max = 225.

A-law Companding

• A-law uses a piecewise characteristic: a linear section for small inputs and a logarithmic section for larger inputs. It is an ITU-T standard and is designed to be easily implemented digitally by approximating the curve by straight line segments.
• The parameter from the source material is given as A_max = 87.6.
• Companding tends to keep the effective signal-to-noise ratio approximately constant across a wide range of signal levels and is especially useful in telephone trunking and other voice systems.

Differential Pulse Code Modulation (DPCM)

• DPCM is a form of PCM that encodes differences (prediction errors) between successive samples rather than the samples themselves. It exploits the correlation between neighbouring samples to reduce the required bit rate for a given quality.
• When the sampled sequence is highly correlated, DPCM provides a bandwidth advantage or allows a higher effective data rate for the same bandwidth.
• Prediction is the principal technique used in DPCM: a predictor estimates the next sample from previous reconstructed samples and the encoder transmits only the difference between the actual sample and the predicted value.
• Two main differential coding schemes are:
  • Delta Modulation (DM);
  • Differential PCM (DPCM) and Adaptive DPCM (ADPCM).

Delta Modulation

• Delta modulation converts an analogue signal, typically speech, into a one-bit digital signal by transmitting only the sign (up/down) of successive differences. It is a special, one-bit case of DPCM.
• In delta modulation the output bit indicates whether the current sample is greater than or less than the previous reconstructed sample.
• Two typical problems in delta modulation are:
  • Slope overload distortion - occurs when the input changes faster than the maximum slope that the modulator can follow with its fixed step size Δ;
  • Granular noise or hunting - occurs when the input is nearly constant and the fixed step causes small oscillations around the true value.

• To mitigate slope overload, an optimum step size Δ can be chosen. The conditions and expressions for the optimum step size appear in the referenced material.

The notation Δ_opt denotes the optimum value of the step size Δ chosen to trade off slope overload and granular noise.

Adaptive Delta Modulation

Adaptive delta modulation (ADM) varies the step size Δ according to the local behaviour of the message signal. If the message is changing rapidly, the step size is increased to avoid slope overload; if the message varies slowly, the step size is reduced to limit granular noise. This adaptive control of Δ improves overall performance compared with fixed-step delta modulation.

• Adaptive schemes include simple step-size adaptation based on recent bit history and more sophisticated predictors that alter step sizes according to error estimates.
• ADM is therefore a practical technique to balance reproduction quality and bit-rate efficiency in low-bit-rate voice coding.

Receiver Operations, Modulation Types and Decoding Notes

• The receiver of a digital communication system commonly performs the following operations: waveform reception, filtering (often matched filtering), sampling (if required), detection or demodulation to symbols, channel decoding to correct errors, and source decoding to reconstruct the original message.
• Common digital modulation families include:
  • Amplitude-shift keying (ASK) - binary or M-ary variations of amplitude modulation for digital data;
  • Frequency-shift keying (FSK) - frequency changes represent symbols;
  • Phase-shift keying (PSK) - phase changes represent symbols, including BPSK, QPSK, and higher-order PSK;
  • Quadrature amplitude modulation (QAM) - combines amplitude and phase modulation to represent multiple bits per symbol and is widely used in modern systems.
• Demodulation techniques seek to determine which transmitted waveform or symbol was most likely sent, based on the received noisy waveform and known waveform set; optimal demodulators often implement correlation or matched filtering followed by a decision rule (for example, maximum-likelihood).
• Error control by channel coding (block codes, convolutional codes, turbo codes, LDPC codes) is essential to achieve reliable communications close to channel capacity; decoders use the introduced redundancy to detect and correct errors before source decoding.
• Performance metrics include bit-error rate (BER), symbol-error rate (SER), and signal-to-noise ratio (SNR); these metrics are used to design trade-offs among bandwidth, power, and complexity.

Applications and Practical Notes

• PCM with companding is the standard technique in digital telephony, where voice is digitised, companded, and encoded at well-defined sampling and bit rates.
• DPCM and ADPCM find use in low-bit-rate speech coding, audio compression and multimedia codecs where correlation between successive samples can be exploited.
• Delta modulation and its adaptive variants are useful in very low-rate voice transmission systems and in simple analog-to-digital converters where complexity must be kept minimal.
• Choosing quantizer resolution (number of bits), sampling rate, modulation format and channel code involves trade-offs among reconstructed quality, spectral bandwidth, transmitted power and system complexity.

Summary

This chapter has described the principal building blocks of a digital communication system and common modulation and coding techniques used to convert analog or discrete sources into reliably transmitted digital signals. Key ideas include source and channel coding, PCM and its quantization, companding methods (μ-law and A-law), DPCM and delta modulation (including adaptive delta modulation), and receiver decoding operations. Understanding the trade-offs among bit rate, quantization noise (SQNR), bandwidth and complexity is essential when designing practical digital communication systems.