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Shannon-Kotel’nikov Mappings for Joint Source-Channel Coding
Thesis Defence Lecture
Fredrik Hekland1. June 2007
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Outline
● Some fundamentals on communications● Shannon-Kotel’nikov mappings● Key results
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Source Coding● Analog sources
Infinite information
● To meet a rate constraint SC can Remove redundancy Remove irrelevancy Reduce perceptual
quality
64kbit/s
RAW: 8MB
JPEG: 1MB87 photos
700 photos
OBJECTIVESMinimize rate given a distortion constraintMinimize distortion given a rate constraint
OBJECTIVESMinimize rate given a distortion constraintMinimize distortion given a rate constraint
13kbit/s
• Processing power
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Channel Coding
InformationInformation Channel
Minimize impact of channel noise,while still trying to maximize channel utilizationMinimize impact of channel noise,while still trying to maximize channel utilization
No channel coding/error protection:
Channel space
Code word
Noise
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Joint or Separate Coding
Source Coder Channel Coder Channel
Rate Allocation
JOINT SOURCE-CHANNEL CODING
- Same performance as separated system, while requiring lower delay/complexity.
- Good performance for a larger range of source-channel pairs.
JOINT SOURCE-CHANNEL CODING
- Same performance as separated system, while requiring lower delay/complexity.
- Good performance for a larger range of source-channel pairs.
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Heterogeneous Networks
● Incompatible communication systems demand transcoding where they interface
Mobile phone
Basestation
ADSL & WLAN
Telephonecentral
Old schooltelephone
PDA withSkype
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Shannon-Kotel’nikov Mappings
● Non-linear mappings Discrete time,
continuous amplitude Robust Low delay
● Bandwidth expansion Noise reduction
● Bandwidth reduction Compression
S1
S2
●
Uncertainty dueto noise
Y1
Y2
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The Guys
Claude E. Shannon Vladimir A. Kotel'nikov
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Research Objectives
● Bandwidth-efficient and robust (lossy) source-channel coding systems
● Transcoding schemes for Shannon-Kotel’nikov mappings How to interface with digital transport networks Determine whether or not joint optimization of
transcoding/mapping is necessary Propose simple and effective schemes
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Assumptions
● Point-to-point channels● Source, S, is independent and identically
distributed● Channel noise, Z, is Additive White Gaussian
Noise (AWGN)
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Key Results
● Description of performance losses in source-channel coding
● Bandwidth reducing mappings● Transcoding of mappings for heterogeneous
networks● Mappings in multi-hop scenarios
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Quantifying Performance Losses in Source-Channel Coding
● Mismatched channel symbol distribution● Mismatched error-sequence distribution● Incorrect assumption of source distributions ● Rate lower than channel capacity● Correlation● Receiver structures● Decoding errors
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Bandwidth-Reducing Mappings
● 2:1 - Gaussian source and AWGN channel
● 2:1 - Laplacian source and AWGN channel Warping LG is a viable
alternative.
● 4:1 through cascading two 2:1 mappings.
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Bandwidth-Reducing Mappings
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Transcoding for Heterogeneous Networks
● Simple scalar quantizer performs well
● Joint optimization of mapping and quantizer
● Quantize either at transmitter or receiver side
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Transcoding for Heterogeneous Networks
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Multi-hop Communication
● Pre-quantized mapping necessary
● Worst link determines performance
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Errata
● P.112, last bullet belongs to Section 5.2.
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Now, unleash the opponents ...