 Linear Codes for Distributed Source Coding: Reconstruction of a Function of the Sources D. Krithivasan and S. Sandeep Pradhan

Yüklə 525 b.
 tarix 20.09.2018 ölçüsü 525 b. • Conclusions • Example: Lossless reconstruction of all sources – joint entropy. • Are rate gains possible if we directly encode the function in a distributed setting? • Centralized encoder:

• Compute
• Compress using a good source encoder

• Are there good source codes with this property?

• Linear Codes. • matrix such that:

• Decoder with high probability.
• Entropy achieving:

• Scheme works for addition in any finite field. • Both encoders use identical codebooks

• Binning completely “correlated”
• Independent binning more prevalent in information theory. • Encode the vector function one digit at a time. • General lossless strategy:

• “Embed” the function in a digit plane field (DPF).
• DPF – direct sum of Galois fields of prime order.
• Encode the digits sequentially using Korner-Marton strategy. • What we need: Nested linear codes. • Codes used in KM, SW – good channel codes

• Cosets bin the entire space.
• Suitable for lossless coding.
• Lossy coding: Need to quantize first.

• Decrease coset density. • Codes used in KM, SW – good channel codes

• Cosets bin the entire space.
• Suitable for lossless coding.
• Lossy coding: Need to quantize first.

• Decrease coset density – Nested linear codes.
• Fine code: quantizes the source.
• Coarse code: bins only the fine code. • We need

• : “good” source code
• :“good” channel code
• Can find unique typical for a given • Not a good source code in the Shannon sense.

• Contains a subset that is a good Shannon source code.
• Linearity – rate loss of bits/sample • Not a good channel code in the Shannon sense.

• Every coset contains a subset which is a good channel code.
• Linearity – rate loss of bits/sample • At bth stage: Use previous reconstructed digits as side information. • Good source codes , good channel code • Conventional coding: • An achievable rate region • Can also recover

• Berger-Tung inner bound.
• Wyner-Ziv rate region.
• Wyner’s source coding with side information.
• Slepian-Wolf and Korner Marton rate regions. • Can achieve more rate points by

• Choosing more general test channels.
• Embedding in • Presents new rate regions for other problems. Dostları ilə paylaş:

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