What is the working principle of Pulse Code Modulation (PCM)?

Working Principle

Pulse Code Modulation is the process of converting a time-continuous, amplitude-continuous analog signal into a time-discrete, amplitude-discrete digital signal for transmission over a channel. PCM involves first sampling the analog signal, then quantizing and encoding the sampled amplitude values.
Sampling is the periodic scanning of an analog signal, converting a time-continuous signal into a time-discrete signal. The sampled analog signal must still contain all the information of the original signal, meaning the original analog signal can be recovered without distortion. The lower limit of the sampling rate is determined by the sampling theorem, and the sampling rate is 8 kbit/s.
Quantization is the process of discretizing the amplitude of the instantaneous values obtained from sampling, i.e., using a set of specified levels to represent each instantaneous sampled value with the nearest level.
After an analog signal is sampled and quantized, a quantized pulse amplitude modulation signal is obtained, which has only a finite number of values.
Encoding is the process of using a set of binary code groups to represent each quantized value with a fixed level. In practice, quantization is completed simultaneously during the encoding process, so the encoding process is also referred to as analog-to-digital conversion, denoted as A/D.

PCM, abbreviated as Pulse Code Modulation, first passes the voice signal through an anti-aliasing low-pass filter, performs pulse sampling to generate a sampling signal with an 8 kHz repetition rate (i.e., a discrete pulse amplitude modulation, PAM, signal), then quantizes the amplitude-continuous PAM signal into a signal with a finite number of amplitude values using a "rounding" method, and finally converts it into binary codes through encoding. For telephony, the CCITT specifies a sampling rate of 8 kHz, with each sampled value encoded into 8 bits, i.e., a total of 2^8 = 256 quantized values. Therefore, the standard digital rate for each voice channel after PCM encoding is 64 kb/s. To address the issues of large quantization error and poor voice quality for small signals in uniform quantization, a non-linear quantization method with non-uniform quantization intervals is adopted in practice, where the quantization characteristic has denser levels and smaller intervals for small signals, and sparser levels and larger intervals for large signals.

In practice, two logarithmic compression characteristics are used: A-law and μ-law. A-law encoding is mainly used in 30/32-channel primary rate systems, while μ-law encoding is mainly used in 24-channel primary rate systems. A-law PCM is used in Europe and China, while μ-law PCM is used in North America and Japan.

PCM Encoding

PCM encoding principles and rules: The PCM digital interface complies with the G.703 standard, transmitting asymmetrically or symmetrically over 75Ω coaxial cable or 120Ω twisted pair. The transmission line code is HDB3 code containing timing information, and the receiving end can recover timing through decoding to achieve clock synchronization. Fb is the frame synchronization signal, C2 is the clock signal at a rate of 2.048 Mbps, and data is valid on the falling edge of the clock. The E1 interface has a PCM frame structure: a multiframe consists of 16 frames, each frame is 125 μs and divided into 32 timeslots. Among these, the zero timeslot of even frames carries the synchronization information code 0011011, the zero timeslot of odd frames carries the remote alarm indication, timeslot 16 carries signaling information, and the other timeslots carry data, with each timeslot transmitting 8 bits of data.