--- title: "Why DPCM over PCM; DPCM transmitter and receiver" subject: "Communication Systems" chapter: 4 key: "semester_6/communication_systems:dpcm-preferred-transmitter-receiver" source: https://www.bctengineer.com/q/semester_6/communication_systems/dpcm-preferred-transmitter-receiver site: BCT Engineering --- # Why DPCM over PCM; DPCM transmitter and receiver Communication Systems · Chapter 4: Pulse Modulation - Asked in: 2075 Asoj (CS II), 2+4 marks; 2071 Chaitra (CS II), 2+5 marks (asked 2 times) - Video: [DPCM Encoder & DPCM Decoder | DPCM Transmitter | DPCM Receiver | Differential Pulse Code Modulation](https://www.youtube.com/watch?v=UjkrvGc3lCo) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/dpcm-preferred-transmitter-receiver - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-4 ## Question Explain why DPCM is preferred over PCM? Explain the working principle of DPCM with necessary transmitter and receiver. ## Short answer DPCM preferred over PCM because correlated samples have redundancy; DPCM quantizes prediction error giving 4-11 dB SQNR gain or lower bit rate. Transmitter predicts sample, quantizes error, encodes, and feeds reconstructed sample to predictor. Receiver decodes error, uses identical predictor, sums to reconstruct signal. ## Answer #### Why DPCM is preferred over PCM Speech and video samples taken at or above the Nyquist rate are **highly correlated**: adjacent samples differ only slightly. PCM codes every sample fully, so it sends much **redundant** information. **DPCM** predicts each sample from past samples and quantizes only the **difference** (prediction error). Since the error has a much smaller range than the signal: - For the same number of bits, the step size is smaller, so **SQNR improves** by the prediction gain $G_p = \sigma_m^2/\sigma_e^2$ (typically 4–11 dB for speech). - For the same SQNR, **fewer bits per sample** are needed, so bit rate and bandwidth are lower (e.g. 32 kbps ADPCM vs 64 kbps PCM). #### DPCM transmitter ```text m[n]-->(+)--e[n]-->[Quantizer]--+--eq[n]->[Encoder]-> ^ - | | v m^[n] (+)<------+ | | mq[n] | +----[Predictor]<-------+ | | | +----------------------+ ``` 1. Prediction error: $e[n] = m[n] - \hat{m}[n]$. 2. Quantized error: $e_q[n] = e[n] + q[n]$, which is encoded and transmitted. 3. The predictor input is the reconstructed sample $m_q[n] = \hat{m}[n] + e_q[n]$. 4. Then $m_q[n] = \hat{m}[n] + e[n] + q[n] = m[n] + q[n]$: the quantized sample differs from the original only by the quantization error of $e[n]$, so errors **do not accumulate**. 5. The predictor (a linear FIR filter, $\hat{m}[n] = \sum w_k m_q[n-k]$) works on $m_q$, the same signal available at the receiver. #### DPCM receiver ```text in->[Decoder]--eq[n]-->(+)--+--> mq[n] -->[LPF]--> m(t) ^ | m^[n]| | +--[Predictor] ``` The decoder recovers $e_q[n]$; the same predictor as in the transmitter gives $\hat{m}[n]$; their sum gives $m_q[n] = m[n] + q[n]$. A low-pass filter reconstructs the analog signal. **Note:** delta modulation is a special case of DPCM with a 1-bit quantizer and a one-sample delay as the predictor. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why does DPCM beat PCM? A. Adjacent samples are highly correlated, so only the small prediction error needs coding B. It removes the need for a quantizer C. It samples below the Nyquist rate D. It uses a larger quantizer step Answer: A. Coding the difference removes redundancy, giving higher SQNR or fewer bits. (Key point: Redundancy) 2. What does prediction gain Gp = sigma_m^2/sigma_e^2 give? A. Increase in bandwidth by Gp B. Reduction in sampling rate by Gp C. SQNR improvement of 10 log Gp dB over PCM with the same bits D. Reduction in the number of samples Answer: C. With the same bits, quantization noise falls by Gp relative to the signal. (Key point: Prediction gain) 3. Why do quantization errors not accumulate in DPCM? A. The predictor is removed at the receiver B. The quantizer has infinite levels C. The predictor works on mq[n] = m[n] + q[n], so only the latest q[n] appears D. The receiver ignores the quantized error Answer: C. Feedback from the reconstructed sample means mq differs from m only by the current quantization error. (Key point: No error accumulation) 4. How does the DPCM receiver rebuild the signal? A. Adds the decoded eq[n] to the prediction from the same predictor, then low-pass filters B. Squares the decoded error C. Multiplies eq[n] by the prediction D. Integrates eq[n] with no predictor Answer: A. mq[n] = m^[n] + eq[n], followed by an LPF. (Key point: Receiver) ## Related in Communication Systems - [Working principle of PCM](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Apcm-working-principle) — 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 - [Stereo FM transmitter and receiver; output of mono receiver](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Astereo-fm-mono-receiver) — Communication Systems, chapter 3 - [Aperture effect, DPCM and DM slope overload numerical](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aaperture-effect-dpcm-dm-slope) — Communication Systems, chapter 4 - [DPCM vs delta modulation; E1 hierarchy](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adpcm-vs-dm-e1) — Communication Systems, chapter 4 - [Companding; DPCM with derivation and block diagram](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acompanding-dpcm) — Communication Systems, chapter 4 ## Related in other subjects - [OFDM transmitter and receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aofdm-transmitter-receiver) — Wireless Communication, chapter 4, asked 5× - [OQPSK transmitter/receiver and π/4-QPSK](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aoqpsk-pi4-qpsk) — Wireless Communication, chapter 4 - [Spread spectrum and DSSS transmitter/receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspread-spectrum-dsss-tx-rx) — Wireless Communication, chapter 4 - [DPSK transmitter/receiver and PN sequence](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adpsk-pn-sequence) — Wireless Communication, chapter 4