Why DPCM over PCM; DPCM transmitter and receiver

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

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

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.