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Side Information Design in Zero-Error Coding for Computing.

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Summary
This summary is machine-generated.

This study explores zero-error coding with side information, focusing on optimizing encoder information quality for better data retrieval rates. We developed algorithms to find optimal trade-offs, with one running in polynomial time.

Keywords:
graph theorysource codingzero-error information theory

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Area of Science:

  • Information Theory
  • Coding Theory
  • Computer Science

Background:

  • Investigates zero-error coding for computing problems where encoders have side information.
  • Builds upon prior work that established conditions for an analytic expression of the optimal rate R*(g).

Purpose of the Study:

  • To analyze the side information design problem, balancing encoder side information quality with optimal coding rates.
  • To develop algorithms for finding achievable trade-offs in this design problem.

Main Methods:

  • Review of existing results on zero-error coding with encoder side information.
  • Development of two greedy algorithms based on partition refining and coarsening for the side information design problem.

Main Results:

  • Identified trade-offs between the quality of encoder side information g(Y) and the optimal rate R*(g).
  • Proposed two greedy algorithms to achieve a set of points in the side information design problem.
  • Demonstrated that one of the developed algorithms operates in polynomial time.

Conclusions:

  • The study provides a framework for optimizing side information in zero-error coding.
  • The developed algorithms offer practical approaches to achieving efficient coding strategies.
  • Efficient polynomial-time algorithms are presented for designing effective side information strategies.