DPCM vs delta modulation; E1 hierarchy

Differential PCM (DPCM)

Adjacent samples of speech and video are highly correlated, so instead of coding each sample, DPCM codes the difference between the sample and a prediction of it. The difference has a smaller range, so fewer bits (or a smaller step) are needed for the same quality.

Transmitter
m[k]->(+)-d[k]->[Quantizer]-dq[k]->[Encoder]-> out
       ^-                  |
       |                   v
   m^[k]<-[Predictor]<-(+)<+
                        ^ m^[k]
Receiver
--> [Decoder] --dq[k]-->(+)--mq[k]--> LPF --> output
                         ^    |
                         +--[Predictor]

• Prediction error: $d[k] = m[k] - \hat m[k]$; quantized: $d_q[k] = d[k] + q[k]$.
• Predictor input: $m_q[k] = \hat m[k] + d_q[k] = m[k] + q[k]$, so the receiver, using the same predictor, rebuilds $m[k]$ with only the quantization error $q[k]$.
• SNR improvement over PCM is the prediction gain $G_p = \overline{m^2}/\overline{d^2}$; typically 4–11 dB for speech, saving 1–2 bits per sample.

DPCM vs Delta Modulation

DM is in fact a 1-bit DPCM.

E1 TDM-PCM telephone hierarchy

E1 is the European (CEPT/ITU-T) primary PCM-TDM system:

• Each voice channel: 8 kHz sampling × 8 bits = 64 kbps.
• One frame = 125 µs with 32 time slots of 8 bits = 256 bits.
• TS0 carries frame alignment, TS16 carries signalling, TS1–15 and TS17–31 carry 30 voice channels.
• Bit rate $= 32 \times 64 = 2.048$ Mbps.

Higher levels combine 4 lower streams each (plus justification bits):