optimal delayed decisions in decoding of predictively ......speech coding via adaptive differential...
TRANSCRIPT
-
Optimal Delayed Decisions
in Decoding of Predictively
Encoded Sources
Vinay Melkote and Kenneth Rose
Signal Compression Lab
Department of Electrical and Computer Engineering
University of California, Santa Barbara
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Signal Compression Lab, ECE, UCSB 2
Introduction
� Decoders simply reconstruct data, no parameter choices to make
� Can decoder delay, and thus accrued future coded data, improve current reconstruction?
� Feasible if adequate correlation exists between coded
data units
� Predictive coding systems provide the right setting:
assume an underlying correlation model for the source
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Signal Compression Lab, ECE, UCSB 3
Introduction
� Predictive coding widely employed in signal compression standards:
� Motion-compensated video coding (H.264)
� Speech coding via adaptive differential pulse code
modulation (G.726, G.722)
� Continuously variable slope delta modulation (Bluetooth hands-free profile)
� Attractive for low-delay/low-complexity applications
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Signal Compression Lab, ECE, UCSB 4
Introduction
� Assume a scalar first-order autoregressive (AR) source: a sequence of zero-mean random variables
that evolve as
1 1, ,n n nx x x− +⋯ ⋯
1n n nx x zρ −= +
( )Zp zi.i.d innovations withzero-mean pdf
nz nx
1zρ −
correlated source samples with inter-sample correlation coefficient ρ
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Signal Compression Lab, ECE, UCSB 5
Introduction
� Consider coding with a differential pulse code modulation scheme (DPCM)
� The prediction here is
� Generally, , i.e., predictor matched to source
1 1, ,n n nx x x− +⋯ ⋯
nx ne
nxɶnxɶ
ni
n̂e
n̂x
+
-
++
Q
nxɶ
n̂en̂x
+1
az−
1az
−
DPCM Encoder
DPCM Decoder
1ˆ
n nx ax −=ɶ
a ρ=
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Signal Compression Lab, ECE, UCSB 6
� DPCM encoder and decoder operate at zero delay
� At asymptotically high bit-rates:
�
� Matched predictor is optimal
�
� Hence indices are approximately i.i.d
� DPCM encoder and decoder operate at zero delay
� At asymptotically high bit-rates:
�
� Matched predictor is optimal
�
� Hence indices are approximately i.i.d
� Future indices provide no information on
� Zero-delay decoder optimal for the given encoder
Introduction
1 1ˆ
n n nx x xρ ρ− −= ≈ɶ
1 1, ,n n ni i i− +⋯ ⋯
1 2, ,n ni i+ + ⋯
1 1ˆ
n n n n n ne x x x x zρ ρ− −≈∴ = − − =
nx
1 1ˆ
n nx x− −≈
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Signal Compression Lab, ECE, UCSB 7
Introduction
� At low bit-rates, prediction errors are correlated, and the indices as well
� Future indices contain information on
� Can this be exploited, by appropriate decoding delay, to
improve the reconstruction of ?
nx
nx
1 1, ,n n ni i i− +⋯ ⋯
1 2, ,n ni i+ + ⋯
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Signal Compression Lab, ECE, UCSB 8
Prior work
� Interpolative DPCM (IDPCM) [Sethia & Anderson, ‘78] and
Smoothed DPCM (SDPCM) [Chang & Gibson, ‘91]
� Apply a non-causal post-filter to smooth the zero-delay
reconstructions: non-causality implemented by delay
Regular zero-
delay DPCM
reconstructions
ˆ ˆ or idpcm sdpcmn nx x
1ˆ
nx + 2ˆnx +1ˆnx − ˆn Lx +2ˆnx − ˆnx
+
n Lb +2nb +1nb +1nb −2nb − n
b
Delayed reconstructions
after filtering
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Signal Compression Lab, ECE, UCSB 9
Prior work
� IDPCM and SDPCM differ in the design of the non-causal
filter
� The IDPCM design:
� Filter taps determined by minimization of an expectedmean squared error that involves statistics of
unquantized samples
� Process autocorrelation determines filter taps
� Ignores bit-rate and innovation densities
� No gains by increasing look-ahead beyond process order
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Signal Compression Lab, ECE, UCSB 10
Prior work
� The SDPCM design:
� Employs a Kalman fixed-lag smoother
� The AR process provides the ‘plant’ model with source samples viewed as the ‘plant state’.
� Quantizer operation provides the ‘observation’ model, with quantized source samples ( ) perceived as ‘observations’
� The model assumes that the quantization noise is white
and uncorrelated with the source
� Kalman filter optimal for linear Gaussian model: ignores the true innovation pdf
ˆnx
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Signal Compression Lab, ECE, UCSB 11
� Decoder has more information: unused by mere averaging of the zero-delay reconstructions
� For instance, decoder has information
� Smoothed reconstructions need not lie in
which is known to the decoder
0
Q
( )na i ( )nb i
( )n n
x a i+ɶ ( )n nx b i+ɶnxɶ
nx+ ɶ lay in this interval ne
lies in this interval= + n n nx x eɶ
Sub-optimalities
( , , )n nx i Qɶ
[ )( ) ( )n n n n nI x a i x b i= + +ɶ ɶ
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12
Proposed method
� Estimation-theoretic approach that optimally combines the
information to obtain the - sample
delayed reconstruction of
� Recursively calculates the pdf of conditioned on all
available information
nx1 1, , , , ,n n n n Li i i i− + +⋯ ⋯
nx
L
ni n̂x ˆsdpcm
nxˆidpcm
nx
Regular DPCM
Decoder
Optimal Delayed
Decoderni n̂x
*
n̂x
IDPCM or SDPCM
Proposed method
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Signal Compression Lab, ECE, UCSB 13
� Distortion criterion - mean squared error (MSE)
� The optimal estimate of at the decoder, with delay
� Intervals are an equivalent
representation of information available to the decoder
� Expectation over the conditional pdf
� Distortion criterion - mean squared error (MSE)
� The optimal estimate of at the decoder, with delay :
Optimal Delayed Decoder
nx L*
1ˆ [ | , , , , ]n n n n n Lx E x i i i− += ⋯ ⋯
1[ | , , , , ]n n n n LE x I I I− += ⋯ ⋯
1( | , , , , )n n n n Lp x I I I− +⋯ ⋯
[ )( ) ( )n n n n nI x a i x b i= + +ɶ ɶ
[Gibson & Fischer, ‘82]
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Signal Compression Lab, ECE, UCSB 14
� By application of Bayes’ rule and Markov property of the process
� is the zero-delay pdf – combines all
information up to time
� weighs the zero-delay pdf to incorporate future information
({ } | )k n k n L np I x< ≤ +
( |{ } )n k k np x I ≤
( |{ } ) ({ } | )( |{ } )
( |{ } ) ({ } | )
n k k n k n k n L nn k k n L
n k k n k n k n L n n
p x I p I xp x I
p x I p I x dx
≤ < ≤ +≤ +
≤ < ≤ +
=
∫
Optimal Delayed Decoder
n
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15
Forward recursion
� Recursion for the zero-delay pdf: update from time to
Say, zero-
delay pdf at
time is
known
1n −
n1n −
1nI −
1 1( |{ } )n k k np x I− ≤ −
1nx −
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16
Time
n-1
1nI −
1 1( |{ } )n k k np x I− ≤ −
1nx −
n
nx
1( )Z n np x xρ −−
Forward recursion
� Recursion for the zero-delay pdf: update from time to n1n −
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17
Time
n-1
1nI −
1 1( |{ } )n k k np x I− ≤ −
1nx −
n
nx
1 1 1( |{ } ) ( )n k k n Z n np x I p x xρ− ≤ − −−
Forward recursion
� Recursion for the zero-delay pdf: update from time to n1n −
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18
1nI −
1 1( |{ } )n k k np x I− ≤ −
1nx −
nx
1 1 1 1 1( |{ } ) ( |{ } ) ( )n k k n n k k n Z n n np x I p x I p x x dxρ≤ − − ≤ − − −= −∫
Forward recursion
� Recursion for the zero-delay pdf: update from time to n1n −
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19
1nI −
1 1( |{ } )n k k np x I− ≤ −
1nx −
nxnI
1( |{ } )
0
n k k n n np x I x I
otherwise
≤ − ∈
Forward recursion
� Recursion for the zero-delay pdf: update from time to n1n −
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20
Time
n-1
1nI −
1 1( |{ } )n k k np x I− ≤ −
1nx −
n
nx
( |{ } )n k k np x I ≤
nI
1
1
( |{ } )
( |{ } )( |{ } )
0
n
n k k nn n
n k k n nn k k n
I
p x Ix I
p x I dxp x I
otherwise
≤ −
≤ −≤
∈
=
∫
Forward recursion
� Recursion for the zero-delay pdf: update from time to n1n −
Zero-delay pdf
at time n
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21
1 1( | ) ( )
n L
n L n L Z n L n L n L
I
p I x p x x dxρ
+
+ + − + + − += −∫
n LI +
1n Lx + −
n Lx +
Backward recursion
� Recursion for the probability of future outcomes: step back from
time to nn L+
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22
1 1( | ) ( )
n L
n L n L Z n L n L n L
I
p I x p x x dxρ
+
+ + − + + − += −∫
n LI +
1n Lx + −
n Lx +Time
n+L-1
n+L
n LI +
1n Lx + −
n Lx +
1 1( | ) ( )
n L
n L n L Z n L n L n L
I
p I x p x x dxρ
+
+ + − + + − += −∫
Backward recursion
� Recursion for the probability of future outcomes: step back from
time to nn L+
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23
n LI +
1n Lx + −
n Lx +
1 1( | ) ( )
n L
n L n L Z n L n L n L
I
p I x p x x dxρ
+
+ + − + + − += −∫
Backward recursion
� Recursion for the probability of future outcomes: step back from
time to nn L+
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24
n LI +
1n Lx + −
n Lx +
1 1( | ) ( )
n L
n L n L Z n L n L n L
I
p I x p x x dxρ
+
+ + − + + − += −∫
Backward recursion
� Recursion for the probability of future outcomes: step back from
time to nn L+
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25
n LI +
1n Lx + −
n Lx +
1( | )n L n Lp I x+ + −
Backward recursion
� Recursion for the probability of future outcomes: step back from
time to nn L+
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26
n LI +
1n Lx + −
n Lx +
1n LI + −
1 1 1( | )
0
n L n L n L n Lp I x x I
otherwise
+ + − + − + −∈
Backward recursion
� Recursion for the probability of future outcomes: step back from
time to nn L+
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27
Time
n+L-1
n+L
n LI +
1n Lx + −
n Lx +
1n LI + −
n+L-2
2n Lx + −
1
1 2 1 1 2 1( , | ) ( | ) ( )
n L
n L n L n L n L n L Z n L n L n L
I
p I I x p I x p x x dxρ
+ −
+ + − + − + + − + − + − + −= −∫
Backward recursion
� Recursion for the probability of future outcomes: step back from
time to nn L+
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28
Time
n+L-1
n+L
n LI +
1n Lx + −
n Lx +
1n LI + −
n+L-2
2n Lx + −
1 2( , | )n L n L n Lp I I x+ + − + −
Backward recursion
� Recursion for the probability of future outcomes: step back from
time to nn L+
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Signal Compression Lab, ECE, UCSB 29
n Li +
time
n1n−2n− 1n+ n L+1n L+ −
n Lx +ɶ
n LI +
Summary
� At time n L+
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Signal Compression Lab, ECE, UCSB 30
n1n−2n− 1n+ n L+1n L+ −
nI 1nI + 1n LI + − n LI +
1 1( |{ } )n l l np x I− ≤ −
Summary
� At time n L+
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Signal Compression Lab, ECE, UCSB 31
n1n−2n− 1n+ n L+1n L+ −
nI 1nI + 1n LI + − n LI +
1 1( |{ } )n l l np x I− ≤ −
( |{ } )n l l np x I ≤
Summary
� At time n L+
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Signal Compression Lab, ECE, UCSB 32
n1n−2n− 1n+ n L+1n L+ −
1nI + 1n LI + − n LI +
( |{ } )n l l np x I ≤
({ } | )l n l n L np I x< ≤ +
Summary
� At time n L+
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Signal Compression Lab, ECE, UCSB 33
n1n−2n− 1n+ n L+1n L+ −
1nI + 1n LI + − n LI +
( |{ } )n l l np x I ≤
({ } | )l n l n L np I x< ≤ +
( |{ } )n l l n Lp x I ≤ +
Summary
� At time n L+
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Signal Compression Lab, ECE, UCSB 34
n1n−2n− 1n+ n L+1n L+ −
1nI + 1n LI + − n LI +
( |{ } )n l l np x I ≤
( |{ } )n l l n Lp x I ≤ +
*ˆnx
Summary
� At time n L+
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Signal Compression Lab, ECE, UCSB 35
Special case: matched predictor
� The L-step recursion for future probabilities can be simplified
� There exists function such that,
� A codebook of the functions can be
constructed
� Recursion can be replaced by codebook access with
, and translation of the function by
1ˆ
n nx xρ −=ɶ
1 , ,( )
Li ixΛ
⋯
1 , ,ˆ({ } | ) ( )
n n Lk n k n L n i i n np I x x x
+ +< ≤ += Λ −
⋯
1, ,n n Li i+ +⋯ ˆnx
1 , ,( )
Li ixΛ
⋯
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Signal Compression Lab, ECE, UCSB 36
Table look-up via ?2 1, , ,n n ni i i− −⋯
Codebook-based Delayed Decoder
� Henceforth, we exclusively consider the matched predictor
� Optimal delayed estimate:
1ˆ
n nx xρ −=ɶ
*
1ˆ [ | , , , , ]n n n n n Lx E x I I I− += ⋯ ⋯
({ } | )k n k n L np I x< ≤ +( |{ } )n k k np x I ≤
Table look-up via 1, ,n n Li i+ +⋯
1 , ,ˆ( )
n n Li i n nx x
+ +Λ −
⋯
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Signal Compression Lab, ECE, UCSB 37
Table look-up via ?2 1, , ,n n ni i i− −⋯
Codebook-based Delayed Decoder
� Henceforth, we exclusively consider the matched predictor
� Optimal delayed estimate:
1ˆ
n nx xρ −=ɶ
*
1ˆ [ | , , , , ]n n n n n Lx E x I I I− += ⋯ ⋯
({ } | )k n k n L np I x< ≤ +( |{ } )n k k np x I ≤
Table look-up via 1, ,n n Li i+ +⋯Growing history of indices precludes an optimal
look-up table for the zero-delay pdf
1 , ,ˆ( )
n n Li i n nx x
+ +Λ −
⋯
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Signal Compression Lab, ECE, UCSB 38
A good approximation is still feasible !
Codebook-based Delayed Decoder
� Henceforth, we exclusively consider the matched predictor
� Optimal delayed estimate:
1ˆ
n nx xρ −=ɶ
*
1ˆ [ | , , , , ]n n n n n Lx E x I I I− += ⋯ ⋯
({ } | )k n k n L np I x< ≤ +( |{ } )n k k np x I ≤
Table look-up via 1, ,n n Li i+ +⋯
1 , ,ˆ( )
n n Li i n nx x
+ +Λ −
⋯
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Signal Compression Lab, ECE, UCSB 39
A good approximation is still feasible !
Codebook-based Delayed Decoder
� Henceforth, we exclusively consider the matched predictor
� Optimal delayed estimate:
1ˆ
n nx xρ −=ɶ
*
1ˆ [ | , , , , ]n n n n n Lx E x I I I− += ⋯ ⋯
({ } | )k n k n L np I x< ≤ +( |{ } )n k k np x I ≤
Table look-up via 1, ,n n Li i+ +⋯
A codebook-based approximation for the optimal delayed estimate
1 , ,ˆ( )
n n Li i n nx x
+ +Λ −
⋯
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Signal Compression Lab, ECE, UCSB 40
� Approximation for the zero-delay pdf:
� Let denote the stationary marginal prediction error pdf - a fixed (time invariant) pdf [Farvardin & Modestino, ’85]
� The pdf of conditioned on past indices is approximated as:
� Thus the zero-delay pdf is just:
Codebook-based Delayed Decoder
1ˆ
n n ne x xρ −= −∵
( )Ep e
2 1 1 1ˆ ˆ( | , , ) ( | ) ( )n n n n n E n np x i i p x x p x xρ ρ− − − −≈ = −⋯
nx
1
1
ˆ( )
ˆ( )( |{ } )
0
n
E n nn n
E n n nn k k n
I
p x xx I
p x x dxp x I
otherwise
ρ
ρ
−
−≤
− ∈ −
≈
∫
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Signal Compression Lab, ECE, UCSB 41
� Approximate delayed estimate:
Codebook-based Delayed Decoder
*
1ˆ [ | , , ,
({ } | )
({ } |
( |{ } )
( |{ }]
),
)
k nn n
n n n n n
n k k n
n k k n
k n
L
n
L n
k n k n L n
p I xx dxx E x I I I
p x I
xx I p dp I x−
< ≤ +
< ≤
≤
+
+≤
= =∫∫
⋯ ⋯
1 , ,ˆ( )
n n Li i n nx x
+ +Λ −
⋯
1
1
ˆ( )
ˆ( )
0
n
E n nn n
E n n n
I
p x xx I
p x x dx
otherwise
ρ
ρ
−
−
− ∈ −
∫
[ )1 1ˆ ˆ( ) ( )n n n n nI x a i x b iρ ρ− −= + +1
ˆ ˆ ˆ ( )n n n nx x e iρ −= +
*
1ˆ ˆ ( , , )n n n n Lx x c i iρ − +≈ + ⋯ Look-up table/codebook
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Signal Compression Lab, ECE, UCSB 42
� Numerical evaluation via and
� Alternative - a training-set based design:
� => is the estimate of
the prediction error at time given the window of indices
� Encoder is fixed: run it on a long enough training set of the
source, and obtain prediction error training set and indices
� Train delayed decoding codebook
Codebook design
( )Ep e
*
1ˆ ˆ ( , , )n n n n Lx x c i iρ − +≈ + ⋯ ( , , )n n Lc i i +⋯
n, ,n n Li i +⋯
1 , ,ˆ( )
n n Li i n nx x
+ +Λ −
⋯
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Signal Compression Lab, ECE, UCSB 43
Results
� Source is first order AR
� DPCM Encoder:
� Rate: first order entropy of output indices
� Employs uniform threshold quantizer: scaled suitably to achieve different rates
� Thresholds fixed by scale-factor, reconstructions optimized iteratively similar to [Farvardin & Modestino, ’85]
� Iterative optimization also provides for codebook approach
� Predictor matched to source
( )Ep e
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Signal Compression Lab, ECE, UCSB 44
0.25 0.5 0.75 1 1.25 1.5 1.75 2-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
Rate (bits/sample)
SN
R g
ain
ov
er
reg
ula
r D
PC
M (
dB
)
IDPCM
SDPCMProposed Optimal Decoder
Proposed Codebook Decoder
L=3
L=1
L=3
L=1
Results
Performance comparison of competing delayed decoders for
a Gaussian source with 0.95ρ =
Performance of
zero-delay DPCM
at different bit-rates
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Signal Compression Lab, ECE, UCSB 45
0.25 0.5 0.75 1 1.25 1.5 1.75 2-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
Rate (bits/sample)
SN
R g
ain
ov
er
reg
ula
r D
PC
M (
dB
)
IDPCM
SDPCMProposed Optimal Decoder
Proposed Codebook Decoder
L=3
L=1
L=3
L=1
Results
Performance comparison of competing delayed decoders for
a Gaussian source with 0.95ρ =
SDPCM with lag of 3
samples, worse at
lower delays
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Signal Compression Lab, ECE, UCSB 46
0.25 0.5 0.75 1 1.25 1.5 1.75 2-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
Rate (bits/sample)
SN
R g
ain
ov
er
reg
ula
r D
PC
M (
dB
)
IDPCM
SDPCMProposed Optimal Decoder
Proposed Codebook Decoder
L=3
L=1
L=3
L=1
Results
Performance comparison of competing delayed decoders for
a Gaussian source with 0.95ρ =
IDPCM, delay
limited to 1 sample
automatically
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Signal Compression Lab, ECE, UCSB 47
0.25 0.5 0.75 1 1.25 1.5 1.75 2-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
Rate (bits/sample)
SN
R g
ain
ov
er
reg
ula
r D
PC
M (
dB
)
IDPCM
SDPCMProposed Optimal Decoder
Proposed Codebook Decoder
L=3
L=1
L=3
L=1
Results
Performance comparison of competing delayed decoders for
a Gaussian source with 0.95ρ =
Codebook-
based approach
using 1 and 3
future indices
Performance curves
for the optimal
delayed decoder
hidden beneath plots
for the codebook
approach
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Signal Compression Lab, ECE, UCSB 48
0.25 0.5 0.75 1 1.25 1.5 1.75 2-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
Rate (bits/sample)
SN
R g
ain
ov
er
reg
ula
r D
PC
M (
dB
)
IDPCM
SDPCMProposed Optimal Decoder
Proposed Codebook Decoder
L=3
L=1
L=3
L=1
Zoom in to see the
performance gap
between optimal
and codebook
approaches
Results
Performance comparison of competing delayed decoders for
a Gaussian source with 0.95ρ =
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Signal Compression Lab, ECE, UCSB 49
0.35 0.45 0.55 0.65 0.75 0.851.35
1.4
1.45
1.5
Rate (bits/sample)
SN
R g
ain
ov
er
reg
ula
r D
PC
M (
dB
)
Proposed Optimal Decoder
Proposed Codebook Decoder
Results
Performance comparison of competing delayed decoders for
a Gaussian source with 0.95ρ =
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Signal Compression Lab, ECE, UCSB 50
0.25 0.5 0.75 1 1.25 1.5 1.75 2-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
Rate (bits/sample)
SN
R g
ain
ov
er
reg
ula
r D
PC
M (
dB
)
IDPCM
SDPCMProposed Optimal Decoder
Proposed Codebook Decoder
L=3
L=1
L=3
L=1
� Performance of SDPCM and IDPCM not guaranteed to be better than zero-delay DPCM
� Proposed approaches at 1 sample delay outperform SDPCM at higher delay (3) : indices contain a lot of information
� At low bit-rates increasing delay provides more gains
Results
Performance comparison of competing delayed decoders for
a Gaussian source with 0.95ρ =
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Signal Compression Lab, ECE, UCSB 51
Results
0.8ρ =
0.25 0.5 0.75 1 1.25 1.5 1.75 2-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
Rate (bits/sample)
SN
R g
ain
ov
er
reg
ula
r D
PC
M (
dB
)
IDPCM
SDPCM
Proposed Optimal DecoderL=3
L=1L=3
L=1
Performance comparison of competing delayed decoders
for a Gaussian source with
� Lower correlation naturally implies lesser to be gained from looking into the future
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Signal Compression Lab, ECE, UCSB 52
Results
Performance comparison of competing delayed decoders for
a source with Laplacian innovations with 0.95ρ =
0.25 0.5 0.75 1 1.25 1.5 1.75 2-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
Rate (bits/sample)
SN
R g
ain
ov
er
reg
ula
r D
PC
M (
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IDPCM
SDPCM
Proposed Optimal Decoder
L=3
L=1
L=1
L=3
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Signal Compression Lab, ECE, UCSB 53
Other contributions
� Codebook approach trades computational complexity for memory
� Proposed an approach for codebook-size reduction via an index mapping technique with very minimal performance loss
� Optimal and codebook approaches readily extended to higher ordersources (equivalence via an appropriate first-order vector AR process)
� Index window employed in the codebook can be extended to includea few past indices: useful in the case of higher order sources
� Training-set based design, and codebook-based operation, particularly attractive for higher order sources (due to to the higher dimensionality involved)
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Signal Compression Lab, ECE, UCSB 54
Summary
� Proposed an estimation-theoretic approach for optimal delayed decoding in predictive coding systems
� Combines all known information at the decoder in a recursively calculated conditional pdf
� Motivates a codebook-based delayed decoder that is nearly optimal even for modest dimensions
� Substantial performance gains compared to prior smoothing/filtering techniques
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Signal Compression Lab, ECE, UCSB 55
Future directions
� Encoder optimization based on the proposed delayed decoder
� Employ delayed reconstructions for prediction via local
decoder
� Delayed decoding in adaptive predictive coding scenarios
� Application for speech/audio coding in Bluetooth systems
� Delayed decoding codebook adaptation techniques