FastVDO Unified 16Bit Framework

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FastVDO Unified 16-Bit Framework

• Pankaj Topiwala
• FastVDO LLC
• Columbia, MD 21046 USA
• pnt_at_fastvdo.com
• JVT-B103

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In the Beginning (April 01)

• April 01 FastVDO showed how H.26L can be made
  fully 16-bit with no loss of performance (M16).
• At SB 4 other proposals also supported 16-bits
• Key lessons learned
• Negligible performance or complexity difference
• Quantization is very flexible! TI/Sharp showed
  that it can be manipulated to make even the tml
  transform into 16-bits
• Quant. memory rqmts can be minimized by
  periodicity
• Proper focus the transform which can limit
  applications
• Quantization can be safely decoupled

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Rapid Growth of Applications

• But the application space of H.26L is growing
• low-rate wireless conversational (28 kb/s 256
  kb/s),
• mid-rate streaming, VOD (64 kb/s 1 Mb/s)
• high-rate TV broadcasting (1- 4 Mb/s)
• high-rate storage for future DVD (5-30 Mb/s)
• Multirate digital cinema (mid-rate, visually
  lossless distribution, and lossless archive 30
  Mb/s, 200 Mb/s, and low Gb/s)
• ultra-high rate HDTV (30 Mb/s low Gb/s)
• lossless medical (similar)
• Entertainment applications poised to dominate.

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Desire

• One framework that fits all applications
• Reduce fragmentation of standard
• Limit proliferation of inconsistent technologies
• Improve interoperability between profiles
• Significantly improve content reuse
• FastVDO introduced such a framework
• Still inadequately understood
• Will now explain concretely

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Motivation

• Similar coding performance as the DCT
• Supporting a 16-bit (or less) architecture
• Low complexity, multiplierless implementation
  (adds, right shifts)
• Invertible integer-to-integer mapping
• In-place computation

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DCT

• Coding gain 7.57 dB Complexity 8 adds, 6
  mults in floating point
• Integer approximation

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Lifting Structure
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Generic 4-Pt Lifting Transform
e
b
f
c
d
Note If a u are dyadic rationals, then this
- is exactly invertible! - has a mult-free def,
multiple ways, and - is very stingy in bit
expansion!
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Generic 4-Pt Inverse Transform
-
-
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Example 1 FastVDO X1 - Hadamard
au1/2 bcdefp1.
Three equivalent implementations - matrix
multiply - mult-free direct (8 adds, 0
scalings) - lifting (also mult-free 8a 2s)
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Example 2 FastVDO X2
a1/2 bcdef1, up-1.
Three equivalent implementations - matrix
multiply - mult-free direct (8 adds, 1
scalings) - lifting (also mult-free 8a 1s)
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Example 3 FastVDO X3
a1/2 bcdef1, p-2,u2/5.
W.K.Cham, 1989. X3 proposed by MS,
Nokia. Non-dyadic numbers mean Non-invertible
transform.
Three equivalent implementations
- matrix multiply - mult-free direct (8 adds,
2 scales) - lifting (but with mults!! or
approx. u)
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Example 4 FastVDO X4
apu1/2 bcdef1.
Note High Coding Gain CG(X4) 7.55 dB CG(DCT)
7.57 dB
Three equivalent implementations
- matrix multiply - mult-free direct (9 adds,
2 scalings) - lifting (also mult-free 8a 3s)
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Example 5 FastVDO X5
a1/2 bcdef1, p7/16, u3/8.
Note High Coding Gain CG(X5) 7.57 dB CG(TML)
7.57 dB CG(DCT) 7.57 dB
Three equivalent implementations - matrix
multiply - mult-free direct (9 adds, 7 scales)
- lifting (also mult-free 10a 5s)
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Detailed Implementation of X5
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Performance-Complexity
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Dynamic Range
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8 x 8 BinDCT
Coding gain 8.77 to 8.82 dB for AR(1) process
with p0.95
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16 x 16 BinDCT
Coding gain 9.4499 dB for AR(1) process with
p0.95
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Lessons Learned

• All transforms considered fall under our rubric
  (other than tml)
• No new transforms introduced in 9 months
• Growing app. list needs transform innovation
• Quantization is very flexible
• Innovations have in fact been made in
  quantization
• Sharp/TI showed that even tml can be made 16-bits
• Quantization can be adapted to transform

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Lessons Learned (2) - TML

• TML transform
• OK for low-complexity, wireless app. using fixed
  hard-wired architectures that need matrix
  multiply
• But unfriendly integers not good for ASIC
• Not optimized for bit preservation, high-rate
  apps.
• Not invertible
• Not generalizable to larger transforms
• Satisfies one transform method only direct
  matrix multiply

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Lessons Learned (3) - Cham

• OK for matrix and mult-free applications
• Notionally adds 6 bits in forward transform
• Needs truncation for higher-bit data
• Likely penalty for high-rate, high-bit sources
• Testing on high-bit data critical
• Is not invertible (lifting not dyadic rational)
• Does not generalize to higher transforms
• Satisfies 2 (of 3) transform methods

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Relative Merits

• General Comparisons
• All contenders match current 32-bit performance
• All offer reduced, nearly identical complexity
• Unique Advantages
• General framework to address broad range of needs
• Very tight bit control
• Demonstrated 16-bits output for 12-bit input, no
  truncation
• Suitable for higher-bit data, and high rates
• Related designs for higher sizes (8-pt, 16-pt)
• Advantages of lifting improve further with size

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Currently No Concensus

• First address the low-complexity, low-rate
  problem
• Consider high-rate problem later, probably with a
  different transform
• If lossless is needed, probably a 3rd transform
• Energy misdirected to date
• Some proponents backed single transforms, assumed
  original
• Tests for performance, complexity metrics
  inconclusive
• Missing the bigger picture support a wide
  variety of apps
• Our vision use a single framework if possible
• Going forward focus on our individual strengths

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Recommendations

• Transform and Quantization can be decoupled
• Adopt the framework
• Prefer downloadable filters
• Innovate in the transforms, goal of 3 transform
  methods
• Finalize in the reflector, adopt in May
• Tailor transform to wide variety of applications
• Transform Activity can work directly in
  conjunction with other groups (e.g., Trans. Size,
  ABT, Interlace, Quantization, )
• Quant can focus on transform adaptation, finer
  quantization, periodicity, etc.

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Recommendations (2)

• Focus transforms on high-quality, high-rate
• Low-complexity case well understood
• High-rate apps just emerging in JVT
• Streaming, VOD
• Broadcast (interlaced)
• Film
• Storage (DVD)
• Higher block sizes
• Review ABT options
• Digital Cinema -- we have data
• Look for synergies with low-complexity case