Chap 2' Predictive Coding

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Chap 2. Predictive Coding

• Zero memory property ?
• If the signal is un-correlated ?The spectral is
  flat (while noise)
• The signal is correlated,
• ? we can remove the predictable part, thus the
  dynamic range of redundancy will be
  smaller.

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• Forward predictive scheme
• In encoder, using s(n) to find the predictor
• In decoder, using the predictor find from encoder
  to predict sq(n)

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• Backward predictive Scheme
• The predictor in encoder and decoder were same
  now.

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• Linear Prediction (LPC)

• Analysis and synthesis

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• Analysis filter all-zero (MA)
• Synthesis filter all-pole (AR)
• Solve the linear prediction coefficients using
  MMSE criterion

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• Solution
• Signal is stationary, or at least short-time
  stationary
• Covariance method
• - windowing
• - solve linear equations set with p equations.

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• Autocorrelation method

• Autocorrelation method (continued)
• Yule-Walker equation

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• Levinson-Durbin Algorithm
• R matrix is Toeplitz ? using the Levinson-Durbin
  Algorithm to solve it!

Conversion between LPC and
reflection coefficient

• In the Levinson-Durbin recursive formula, k is
  the reflection coefficients in the Lattice form
  (or Partial correlation coefficientPARCOR)

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• Levinson-Durbin recursive formula (continued)

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• Tube Model log-area ratio

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• Implementation
• - windowing function Hamming window

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• Adaptive one-word memory quantizer (APCM)
• - adjust quantization step
• For mid-raise quantizer

Example of R3
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• Block diagram

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• Performance

The adaptive PCM can have more SNR in signal range
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• DPCM

Input
Output
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• AR (Autoregressive), MA (Moving Average) predictor

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• Using Least Mean Square Error (LMS) method- for
  AR
• ARMA predictor

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• 32Kbps G.721

d(k)
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• Because the dynamic range is smaller for DPCM,
  4-bit adaptive non-uniform quantizer was used.
• log(d(k))-y(k) were sent to Q, output is I()
• ed(k)/y(k) is quantized

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• Adaptive quantizer

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• Adaptation speed control

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• Adaptive predictor 6 zeros, 2 poles ARMA model
• Solution using LMS was shown in slide-11, but in
  order to reduce computation power

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• Performance Segmental SNR (15-25ms)
• The performance is depend on the prediction gain
  (prediction error power/signal power)

• G. 727 Embedded
• Varieties bit-rate, suitable for packetized voice
  protocol (PVP), bit-rate 16, 24, 32, 40 kbps.
• Only 2 bits was used to adjust the quantization
  step size core bits, in receiver the bit can be
  masking to archived the lower bit-rate.

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• Adaptive quantizer in G.727(16 kbps, 2 core bits)

• Performance of G.727 why SSNR?
• prediction gain will be smaller for silence
  (noise)
• 
  larger for voiced signal.

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(m,n) m-bit in AQ, n core bits
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• SSNR of G.727 in different bit-rate

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• Theorematic upper bound