North American T1 vs European E1 hierarchy

The North American (T/DS) hierarchy (AT&T/ANSI) and the European E hierarchy (CEPT/ITU-T G.732/G.751) are the two plesiochronous digital hierarchies (PDH). Both sample each voice channel at 8 kHz with 8-bit PCM (64 kbps) and use a 125 µs frame, but they differ in frame size, signalling and the multiplexing steps.

North American T1 frame

24 channels × 8 bits + 1 framing bit per frame.

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

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

Signalling is "robbed bit": the least significant bit of each channel in every 6th frame (12-frame superframe D4, or 24-frame ESF).

European E1 frame

32 time slots × 8 bits; TS0 for frame alignment, TS16 for signalling (CAS) and TS1–15, TS17–31 for 30 voice channels.

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

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

North American hierarchy

24 x DS0 --> [MUX] --> T1  1.544 Mbps (24 ch)
 4 x T1  --> [M12] --> T2  6.312 Mbps (96 ch)
 7 x T2  --> [M23] --> T3  44.736 Mbps (672 ch)
 6 x T3  --> [M34] --> T4  274.176 Mbps (4032 ch)

European hierarchy

30 x 64k --> [MUX] --> E1  2.048 Mbps (30 ch)
 4 x E1  --> [MUX] --> E2  8.448 Mbps (120 ch)
 4 x E2  --> [MUX] --> E3  34.368 Mbps (480 ch)
 4 x E3  --> [MUX] --> E4  139.264 Mbps (1920 ch)
 4 x E4  --> [MUX] --> E5  564.992 Mbps (7680 ch)

Extra bits at each higher level carry frame alignment, stuffing (justification) and control, as the tributaries are not exactly synchronous.

Comparison

The E system wastes no voice bits on signalling and has a regular ×4 structure; the T system gives slightly higher efficiency at the primary level (only 8 kbps overhead) but degrades voice LSBs. Interworking needs converters (e.g. µ-law ↔ A-law).