TDM and T1/E1 carrier standards

Time Division Multiplexing (TDM) is a technique in which several signals share one transmission line by taking turns in time: each channel is given a short time slot in a repeating frame and uses the whole bandwidth of the line during its slot. For voice, each channel is sampled at 8 kHz and coded into 8-bit PCM words, so a frame lasts 125 µs.

T1 carrier (North American DS1)

• 24 voice channels, each 8 bits per frame, plus 1 framing bit.

 1 bit  8 bits  8 bits        8 bits
+-----+-------+-------+-----+--------+
|  F  |  Ch1  |  Ch2  | ... |  Ch24  |
+-----+-------+-------+-----+--------+
<--------- 193 bits in 125 us -------->
F = framing bit

$$\begin{aligned} \text{Bits per frame} &= 24 \times 8 + 1 = 193\ \text{bits} \\ \text{Frame rate} &= 8000\ \text{frames/s}\ (T = 125\ \mu\text{s}) \\ R_{T1} &= 193 \times 8000 = 1.544\ \text{Mbps} \end{aligned}$$

• Framing: the F bits of successive frames form a fixed pattern (in the 12-frame D4 superframe, 100011011100) used to find frame boundaries.
• Signalling: robbed-bit; in frames 6 and 12 the LSB of each channel carries signalling (A and B bits), so voice uses 7⅚ bits on average.
• Companding: µ-law, $\mu = 255$.
• Line code: bipolar AMI, with B8ZS to avoid long zero runs; 1.544 Mbps over twisted pair with repeaters about every 1.8 km.
• Efficiency: $24 \times 64 = 1.536$ Mbps payload, only 8 kbps overhead.

E1 carrier (European CEPT-1)

• 32 time slots of 8 bits each.

+-----+-----+-----+------+------+-----+------+
| TS0 | TS1 | ... | TS15 | TS16 | ... | TS31 |
+-----+-----+-----+------+------+-----+------+
 sync  <-voice 1-15->  sig   <-voice 16-30->
<------ 32 x 8 = 256 bits in 125 us ------->

$$\begin{aligned} \text{Bits per frame} &= 32 \times 8 = 256\ \text{bits} \\ R_{E1} &= 256 \times 8000 = 2.048\ \text{Mbps} \end{aligned}$$

• TS0: frame-alignment word (0011011) in alternate frames, alarms and spare bits in the others.
• TS16: channel-associated signalling, shared among 30 channels over a 16-frame multiframe (4 bits per channel per multiframe), or used as a 64 kbps common-channel signalling link.
• Voice: TS1–TS15 and TS17–TS31 = 30 channels.
• Companding: A-law ($A = 87.6$). Line code: HDB3.

Comparison summary

Higher levels are formed by multiplexing: 4 T1 → T2 (6.312 Mbps), 7 T2 → T3 (44.736 Mbps); 4 E1 → E2 (8.448 Mbps), 4 E2 → E3 (34.368 Mbps).