Dpcm

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  • Topic: Signal processing, Coding theory, Huffman coding
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  • Published : February 26, 2012
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DPCM - Overview
Principle of Differential Pulse Code Modulation (DPCM) Characteristics of DPCM quantization errors Predictive coding gain Adaptive intra-interframe DPCM Conditional Replenishment

Bernd Girod: EE398B: Image Communication II

DPCM no. 1

Principle of DPCM
input s + e quantizer + s predictor + s' e' entropy coder channel

coder

output

s' + predictor s

+ e'

entropy decoder

channel

decoder

Prediction error

Reconstruction

Reconstruction error = quantization error

e= s−s ˆ

s ′ = e′ + s ˆ

s′ − s = e′ − e = q
DPCM no. 2

Bernd Girod: EE398B: Image Communication II

Quantization error feedback in the DPCM coder
Assuming a linear predictor, the DPCM coder is equivalent to the following structure: ~ s + e e quantizer e' predictor s (s) s (q) predictor q (e) +

Transfer function of the prefilter:

˜ E (Ω) = [1 − P(Ω)]S(Ω)

Ω - abbreviation for frequency vector, ω e.g., ( x , ω y )

transfer function of the predictor

Transfer function of quantization error feedback:

˜ E ′(Ω) = E(Ω) + [1 − P(Ω)]Q(Ω)
Bernd Girod: EE398B: Image Communication II DPCM no. 3

Power spectrum of the DPCM quantization error
Power spectral density of the quantization error q measured for intraframe DPCM with a 16 level quantizer

π
−π
0
0

ωx

ωy

π −π

Bernd Girod: EE398B: Image Communication II

DPCM no. 4

Signal distortions due to intraframe DPCM coding
Granular noise: random noise in flat areas of the picture Edge busyness: jittery appearance of edges (for video) Slope overload: blur of high-contrast edges, Moire patterns in periodic structures.

Bernd Girod: EE398B: Image Communication II

DPCM no. 5

Example of intraframe DPCM coding

1 bit/pixel prediction error coding slope overload

2 bit/pixel edge busyness granular noise

3 bit/pixel

Linear predictor:

0 1/2

1/4 1/4

4 bit/pixel

original

Lloyd-Max quantizers Fixed-length coding
DPCM no. 6

Bernd Girod: EE398B: Image Communication II

Recall from EE398A: High-rate performance of scalar quantizers High-rate distortion-rate function

d ( R) ≅ ε σ 2
2 2 X
Scaling factor ε
2

−2 R

Shannon LowBd Uniform Laplacian Gaussian 6 ≅ 0.703 πe e ≅ 0.865

Lloyd-Max 1 9 = 4.5 2 3π ≅ 2.721 2

Entropy-coded 1 e2 ≅ 1.232 6 πe ≅ 1.423 6
DPCM no. 7

π

1

Bernd Girod: EE398B: Image Communication II

Predictive coding gain
Distortion-rate function with DPCM

d DPCM ( R ) ≅ ε e2σ e2 2−2 R
Prediction gain

Variance of prediction error

GDPCM

ε s2σ s2 = 2 2 εeσ e

Smallest achievable prediction error variance for N-dimensional signal determined by spectral flatness

 1  σ e2 = exp  ln ( Φ xx ( Ω ) ) d Ω  N ∫  ( 2π ) Ω    Bernd Girod: EE398B: Image Communication II DPCM no. 8

Predictive coding gain (cont.)
Consider 1-D Gaussian Markov-1 process with correlation coefficient ρ k 2 Autocorrelation function E [ S n S n − k ] = σ s ρ Prediction gain

GDPCM

1 = 1− ρ 2

Bernd Girod: EE398B: Image Communication II

DPCM no. 9

R-D curves for Gauss-Markov-1 source
SNR [dB] = 10log10

σ2
D

35 30 25 20 15 10 5 0 0 1 2 3

• Linear predictor order

N=1, a=0.9
• Entropy-Constrained Scalar Quantizer with Huffman VLC • Iterative design algorithm applied

R(D*), ρ=0.9 DPCM & ECSQ Panter & Dite App Entropy-Constrained Opt. 4 5 6
DPCM no. 10

7

R [bits]
Bernd Girod: EE398B: Image Communication II

Prediction example: test pattern
original
0
0.95

0

0

0 0

0.95

0

0
0.5

0.5

0

Bernd Girod: EE398B: Image Communication II

DPCM no. 11

Prediction example: Cameraman
original
0
0.95

0

0

0 0

0.95

0

0
0.5

0.5

0

Bernd Girod: EE398B: Image Communication II

DPCM no. 12

Histograms: Cameraman
Image signal
3000 2500 2000 1500 1000 500 0 0 50 100 150 200 250 0.5 0 x 10 2 1.5 1 4

Prediction error
0
0.5 0.5

0

-50

0

50

Bernd Girod: EE398B: Image...
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