1 Shannon-Kotel’nikov Mappings for Joint Source- Channel Coding Thesis Defence Lecture Fredrik Hekland 1. June 2007.

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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 ...