Pulse stuffing and complete TDM PCM system

Multiplexing is combining several signals into one composite signal for transmission over a single shared channel, and separating them again at the receiver.

Why pulse stuffing is needed

When digital tributaries with independent clocks (e.g. four E1 streams entering an E2 multiplexer) are combined, their bit rates differ slightly. The multiplexer reads them at a fixed, slightly higher rate; without correction its input buffers would run empty, causing slips (lost or repeated bits). Pulse stuffing inserts dummy bits whenever a tributary's buffer runs low; stuffing control bits (repeated and decided by majority vote) tell the demultiplexer which bits to remove, so the original stream and clock are recovered exactly. This is why $E2 = 8.448 > 4 \times 2.048$ Mbps.

TDM of analog sources

Analog signals are band-limited, then sampled in turn by a rotating switch (commutator) to give an interleaved PAM signal; each sample is usually quantised and coded (PCM).

• Example: 4 voice channels, each limited to 3.4 kHz and sampled at 8 kHz, give $4 \times 8000 = 32\,000$ samples/s on the line. With 8-bit coding: $32\,000 \times 8 = 256$ kbps.
• If sources have different bandwidths, a wider-band source is sampled several times per frame (super-commutation) and a narrow-band source only once every few frames (sub-commutation), so each sampling rate is a multiple or sub-multiple of the frame rate.

TDM of digital sources

Digital sources are already in bits, so they are interleaved directly, bit by bit or word by word.

• If all sources have the same rate, each gets one slot per frame: 4 sources of 64 kbps → 256 kbps.
• If rates differ but are multiples, faster sources get more slots per frame. Example: sources of 64, 64 and 128 kbps → frame with slots A, B, C, C → 256 kbps.
• If rates are not exact multiples or not synchronous, pulse stuffing is used to bring each to its slot rate.

Complete TDM–PCM system with data rates (T1, 24 channels)

 ch1 -[LPF]-\
 ch2 -[LPF]--[sampler 8 kHz]--[u-law 8-bit coder]
 ch24-[LPF]-/  (commutator)            |
                      [add F bit, AMI/B8ZS]
                                       |
              line 1.544 Mbps, regenerative repeaters
                                       |
 ch1..ch24 <-[LPF]<-[distributor]<-[decoder]<-[frame sync]

Data rates at each stage:

$$\begin{aligned} \text{Samples per channel} &= 8000\ \text{s}^{-1} \\ \text{Channel rate} &= 8000 \times 8 = 64\ \text{kbps} \\ \text{Frame} &= 24 \times 8 + 1 = 193\ \text{bits per } 125\ \mu\text{s} \\ \text{Line rate} &= 193 \times 8000 = 1.544\ \text{Mbps} \end{aligned}$$

The receiver locks onto the framing bits, splits the 8-bit words to the 24 channels, decodes and expands them, and low-pass filters to recover speech. Four such T1 streams, with pulse stuffing, form a T2 at 6.312 Mbps.