---
title: "DPCM vs delta modulation; E1 hierarchy"
subject: "Communication Systems"
chapter: 4
key: "semester_6/communication_systems:dpcm-vs-dm-e1"
source: https://www.bctengineer.com/q/semester_6/communication_systems/dpcm-vs-dm-e1
site: BCT Engineering
---

# DPCM vs delta modulation; E1 hierarchy

Communication Systems · Chapter 4: Pulse Modulation

- Asked in: 2080 Baisakh (CS II), 5+5 marks
- Video: [DIGITAL MULTIPLEXING](https://www.youtube.com/watch?v=q3PtzR9kp9U) — Prof. Barapate's Tutorials
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/dpcm-vs-dm-e1
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-4

## Question

Explain Differential Pulse Code Modulation (DPCM) and compare with Delta Modulation. Explain E1 TDM-PCM Telephone Hierarchy.

## Short answer

DPCM codes the quantized error from a linear predictor, gaining 4–11 dB over PCM. DM is 1-bit DPCM with a simple integrator but requires higher sampling rate. E1 hierarchy: 30 voice channels at 64 kbps each, 2.048 Mbps; higher levels up to 565 Mbps (E5).

## Answer

#### 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.

```text
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**

| Point | DPCM | DM |
|---|---|---|
| Bits per sample | Several (e.g. 3–6) | 1 |
| Quantizer levels | Many | 2 ($\pm\Delta$) |
| Predictor | Linear predictor (higher order) | Simple delay (1st order, integrator) |
| Sampling rate | Near Nyquist | Much higher than Nyquist |
| Slope overload | Rare | Main problem |
| Granular noise | Small | Larger for fixed $\Delta$ |
| Complexity | Higher | Very simple |

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):

| Level | Channels | Bit rate |
|---|---|---|
| E1 | 30 | 2.048 Mbps |
| E2 (4 × E1) | 120 | 8.448 Mbps |
| E3 (4 × E2) | 480 | 34.368 Mbps |
| E4 (4 × E3) | 1920 | 139.264 Mbps |
| E5 (4 × E4) | 7680 | 564.992 Mbps |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why does DPCM need fewer bits than PCM for the same quality?
   A. It samples at a lower rate
   B. It codes the small difference between a sample and its prediction
   C. It uses companding
   D. It transmits only every second sample
   Answer: B. Adjacent samples are correlated, so the prediction error has a smaller range and needs fewer bits. (Key point: DPCM principle)

2. In DPCM, mq[k] = m[k] + q[k]. What does this show?
   A. Errors accumulate with time
   B. The reconstructed sample differs from the true one only by the quantization error of that step
   C. The receiver needs no predictor
   D. The prediction gain is zero
   Answer: B. Because the predictor works on reconstructed values, the only error is the current quantization error. (Key point: Reconstruction error)

3. Which statement correctly compares DM with DPCM?
   A. DM uses several bits per sample and DPCM uses one
   B. DM is 1-bit DPCM and samples much faster than Nyquist
   C. DM has no slope overload but DPCM has
   D. DM uses a higher-order predictor than DPCM
   Answer: B. DM sends 1 bit per sample with a simple first-order predictor and a high sampling rate; slope overload is its main problem. (Key point: DPCM vs DM)

4. An E1 frame has 32 time slots of 8 bits each in 125 µs. The bit rate is:
   A. 1.544 Mbps
   B. 2.048 Mbps
   C. 8.448 Mbps
   D. 64 kbps
   Answer: B. 32 x 8 bits x 8000 frames/s = 2.048 Mbps. (Key point: E1 frame)

## Related in Communication Systems

- [T1 and E1 TDM-PCM hierarchy with frame diagrams](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3At1-e1-frame-diagrams) — Communication Systems, chapter 5
- [FDM vs TDM; FDM telephone hierarchy](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afdm-vs-tdm-fdm-hierarchy) — Communication Systems, chapter 5
- [E1 hierarchy; PCM of 4.2 MHz TV signal with 512 levels](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ae1-pcm-tv-4-2mhz-512) — Communication Systems, chapter 4
- [PCM, DPCM and DM comparison; SQNR of PCM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apcm-dpcm-dm-compare-sqnr) — Communication Systems, chapter 4
- [Delta modulation encoder/decoder; PCM vs DM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adm-encoder-decoder-pcm-vs-dm) — Communication Systems, chapter 4
- [T1 and E1 bit rate and bandwidth; DPCM encoder](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3At1-e1-bitrate-dpcm) — Communication Systems, chapter 5

## Related in other subjects

- [E1 telephone hierarchy](https://www.bctengineer.com/question.md?key=semester_7%2Fcomputer_networks_and_security%3Ae1-hierarchy) — Computer Networks and Security, chapter 2
- [Pulse stuffing and complete TDM PCM system](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Amultiplexing-pulse-stuffing-tdm-pcm) — Telecommunications, chapter 3
- [North American T1 vs European E1 hierarchy](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3At1-e1-hierarchy-compare) — Telecommunications, chapter 3, asked 2×
- [Telephone exchange and switching hierarchy](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aexchange-switching-hierarchy) — Telecommunications, chapter 1, asked 3×