Telecommunications Network Engineering: PCM Coding, Speech Methods, and Power Levels

Structure of the Eight-Bit Binary Word in European PCM (A-law)

• The structure of the 8-bit binary word used in European Pulse Code Modulation (PCM) coding, known as the A-law, is defined by specific bit functions:

  • Bit 1 (Most Significant Bit - MSB): This is the first bit in the sequence and indicates the polarity of the sample.

    • A value of $1$ represents positive polarity.

    • A value of $0$ represents negative polarity.

    • The sample value of zero can produce two distinct code words depending on whether it is interpreted as having positive or negative polarity.

  • Bits 2, 3, and 4: These three bits define the specific segment where the sample value is located.

    • Segments indexed as $000$ and $001$ together form a linear curve designated for low-level positive or negative samples.

    • The complete A-law curve consists of $13$ linear sections (as illustrated in Figure 3.14).

  • Bits 5, 6, 7, and 8 (Least Significant Bits - LSBs): these bits reveal the specific quantized value of the sample within its assigned segment.

    • Each segment is divided linearly into $16$ distinct values or quantum levels.

• Coding Relationship and Compression:

  • The relationship between signal values and binary words is nonlinear, combining nonlinear compression with linear coding.

  • The vertical axis is linear; each binary word corresponds to a quantum level at an equal distance from the others.

  • Linear quantizing is performed on the compressed signal.

  • The relationship between the vertical and horizontal axes follows a logarithmic scale according to equation (3.9).

  • To reduce quantizing noise at low signal levels, half of the quantum levels are dedicated to signal levels smaller than $6.25\%$ (or $\frac{1}{16}$) of the maximum value.

• Bit Inversion and Synchronization:

  • Following the encoding process, every other bit of the resulting code words is inverted prior to multiplexing.

  • The purpose of this inversion is to "mix" the digital signal, facilitating easier timing for line systems and equipment interfaces.

  • For instance, a small negative value producing the code word $00000000$ would be inverted to $01010101$.

  • Without this inversion, transmitting continuous zeros could lead to synchronization difficulties for the receiver.

PCM Encoder and Decoder Standards

• Historical Context: PCM coding schemes for digital voice communications were standardized by the CCITT (now ITU-T) in the early 1970s based on contemporary technology.

• Regional Variations:

  • The European standard (A-law) differs slightly from the American standard (u-law), necessitating conversion equipment for trans-Atlantic or European-to-Japanese communications.

  • The majority of countries worldwide utilize the European A-law standard.

The PCM Encoder Process

• Filtering: Before encoding, the analog signal passes through a lowpass filter (LPF) limiting the frequency band to $300$ to $3,400\,Hz$. This bandwidth is sufficient for human voice recognition and speaker identification.

• Sampling Theorem Compliance: This filtering ensures the sampling theorem is satisfied by removing frequencies higher than half the sampling frequency ($f_s/2$).

• Encoding Steps:

  • The signal is sampled at an $8\,kHz$ sampling frequency.

  • A sample-and-hold (S/H) circuit captures the values.

  • A $256$-level quantizer and encoder convert samples into 8-bit nonlinearly coded words.

  • Parallel words are converted to a serial form via a parallel-to-serial converter.

• Multiplexing and Data Rates:

  • Individual $64\,Kbps$ serial channels are multiplexed using Time Division Multiplexing (TDM).

  • According to the European standard, $30$ voice channels are combined into a $2,048\,Kbps$ (or $2\,Mbps$) primary rate signal.

  • Digital exchanges often build $2\,Mbps$ streams with $30$ PCM-coded subscriber interfaces for internal transmission.

• United States DS1 System:

  • The data rate is $1.544\,Mbps$ instead of $2.048\,Mbps$.

  • Each frame contains $24$ speech channels plus a single framing bit.

  • The math for the data rate is defined as:     $8,000 \times (8 \times 24 + 1) = 1,544,000\,bps = 1.544\,Mbps$

The PCM Decoder Process

• Demultiplexing: The receiver uses a TDM demultiplexer to separate the $2,048\,Kbps$ stream back into individual $64\,Kbps$ channels.

• Reconstruction:

  • The serial signal is converted back to $8$-bit parallel sample values.

  • A decoder reconstructs the sample pulses.

  • A lowpass filter (LPF) smooths the pulses to recreate a voice signal resembling the original analog input.

Advanced Speech-Coding Methods

• Efficiency Definition: "More efficient" indicates achieving better quality at the same data rate or maintaining equal quality at a lower data rate.

• Categories of Coding:

  • Waveform Coding (e.g., PCM): Transmits information describing the signal waveform in the time domain. It adds minimal delay and provides high quality but requires higher data rates.

  • Voice Coding (Vocoders): Utilizes human voice characteristics by modeling segments (e.g., $50\,ms$) and sending model identification codes. Vocoders introduce analytical delay and may split voice into frequency components.

  • Hybrid Coders: Combines waveform and voice coding principles for a compromise between quality and data rate.

• Adaptive PCM (APCM):

  • Transmits signal strength information periodically alongside sample values.

  • Fewer bits are required for samples, as they define the quantum level within a variable scale.

  • Keeping the SQR (Signal-to-Quantizing Ratio) high over a wide range of signal levels.

• Differential PCM (DPCM):

  • Only the difference between a current sample and the previous value is encoded.

  • Since differences are typically small, fewer bits are needed (e.g., $4$ bits instead of $5$ bits).

  • Prediction: Can use multiple preceding samples (typically up to three) to predict the next value; the encoder only transmits the difference between the prediction and the actual sample.

• Delta Modulation (DM):

  • A simplified DPCM that transmits a binary $1$ if the sample increases and a binary $0$ if it decreases.

  • Continuous Variable Slope Delta (CVSD) Modulation: Uses large quantizing steps for steep slopes and small steps for minimal changes. Used in Bluetooth and military applications.

• Adaptive DPCM (ADPCM):

  • Combines APCM and DPCM, adapting both the predictor and the quantizer.

  • Quantization Scaling: If the prediction error increases, the step size doubles; if it decreases, the step size is reduced.

  • Standard Rates: Commercial voice quality is often achieved at $32\,Kbps$ (using $4$ bits per sample at $8\,kHz$), but can go as low as $16$ or $24\,Kbps$.

  • ITU Recommendation G.728: Covers $16/24/32/46-Kbps$ ADPCM and acts as a "common language" between European and North American PCM formats.

  • ITU Recommendation G.722: Codes $7.1\,kHz$ audio into $64\,Kbps$ for high-quality ISDN speech.

  • Applications: Submarine systems, PABX leased lines (doubling capacity), and DECT cordless phones.

  • Limitation: Does not support modems or faxes above $4,800\,bps$.

GSM Speech Coding

• Motivation: Cellular networks require efficient coding to maximize radio frequency usage.

• Implementation:

  • A hybrid principle restricting processing delay to $\le 65\,ms$.

  • Original data rate was $13\,Kbps$, reduced to $7\,Kbps$ in 1995.

  • The voice signal is divided into $20\,ms$ slices.

  • An analysis filter identifies and subtracts the periodical high-power component, which is sent as parameters.

  • The remaining low-level error signal is waveform coded using APCM.

  • A synthesis filter at the receiver reconstructs the speech using the transmitted coefficients.

Quality Measurement and Network Constraints

• Mean Opinion Score (MOS): A measurement based on human opinions of quality ranging from 1 (Bad) to 5 (Excellent).

  • G.711 PCM is typically rated as Excellent.

  • Vocoders often sound synthetic and represent a lower MOS.

• Path Delay Constraints:

  • Round-trip delay should be less than $150\,ms$ for high quality.

  • Deterioration is noticeable once delay exceeds $180\,ms$.

  • Geosynchronous satellites have a one-way delay of approximately $250\,ms$.

  • Echo is noticeable if delay exceeds $30$ to $50\,ms$.

• Echo Cancellers: Required for long delays (satellites or GSM coding) or nonideal return loss in 4W/2W hybrids.

Power Levels and Decibels (dB)

• Definition of Decibel (dB): A logarithmic measure of power change.

  • Gain formula: $g_{dB} = 10 \log_{10}(\frac{P_{out}}{P_{in}})$

  • Loss is represented as negative gain (e.g., an absolute loss of $1/10$ is $-10\,dB$).

  • Gains in a chain are added (e.g., a gain of $100,000,000$ is $80\,dB$).

• Voltage Gain Formula: If impedances differ:     $g_{dB} = 20 \log_{10}(\frac{V_{out}}{V_{in}}) + 10 \log_{10}(\frac{Z_{in}}{Z_{out}})$

• Absolute Power Level (dBm): Power relative to $1\,mW$.

  • $P_{dBm} = 10 \log_{10}(\frac{P}{1\,mW})$

  • Output power level calculation: $P_{out,dBm} = P_{in,dBm} + g_{dB}$.

• Engineering Example (Radio Relay):

  • $P_1 = 1\,W \rightarrow +30\,dBm$ (since $10 \log_{10}(1000/1) = 30$).

  • $P_2 = +30\,dBm + 30\,dB - 110\,dB + 30\,dB = -20\,dBm$.

  • $-20\,dBm$ converts back to $10\, \mu W$.

The Digital Milliwatt

• Purpose: A reference signal for analog levels in the network to ensure compatibility across international digital connections.

• Definition: A specific sequence of 8 code words that, when decoded, produces a $1\,kHz$ sine wave at $0\,dBm$ power level.

• dBm0: The measured signal power level compared to the reference level generated by the digital milliwatt.

• Reference Rules:

  • Standard overload threshold for PCM coder is $+3.14\,dBm0$.

  • Average speech level in an analog channel is approximately $-15\,dBm$.

  • European PCM digital milliwatt requires inverting bits 2, 4, 6, and 8 of the 8-word sequence.

  • Calibration involves adjusting internal amplifiers/attenuators so that $0\,dBm$ input produces $0\,dBm$ output at the decoder.