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An Umbrella Converse for Data Exchange: Applied to Caching, Computing, and Shuffling.

Prasad Krishnan1, Lakshmi Natarajan2, V Lalitha1

  • 1Signal Processing & Communications Research Center, International Institute of Information Technology Hyderabad, Hyderabad 500032, India.

Entropy (Basel, Switzerland)
|August 27, 2021
PubMed
Summary

This study introduces a general converse for data exchange problems, optimizing communication load in multi-user systems like coded caching. The new bound efficiently recovers known results and offers improved bounds for heterogeneous coded caching scenarios.

Keywords:
coded cachingcoded data shufflingcoded distributed computingconversedata exchangeindex coding

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Area of Science:

  • Information Theory
  • Computer Science
  • Network Communication

Background:

  • Multi-user communication problems like coded caching, data shuffling, and coded computing involve optimizing data exchange between nodes with storage and communication capabilities.
  • The primary goal is to minimize the total communication load required for successful data retrieval.

Purpose of the Study:

  • To present a generalized converse for arbitrary data exchange problems, applicable to various multi-user communication scenarios.
  • To derive a new, more encompassing converse for coded caching with heterogeneous cache sizes.
  • To connect the generalized converse to existing bounds in index coding.

Main Methods:

  • Formulating a generic data exchange problem to encompass various existing problems.
  • Developing a novel converse based on the number of bits transferred between node subsets.
  • Applying the generic converse to specific instances like coded caching and coded computing.
  • Deriving a new converse for coded caching with heterogeneous client cache sizes.
  • Relating the centralized version of the bound to the generalized independence number bound in index coding.

Main Results:

  • A general converse for data exchange problems is derived, dependent only on inter-subset data transfer volumes.
  • Known converses for coded caching, data shuffling, and coded computing are efficiently recovered using the generic converse.
  • A new general converse for coded caching with heterogeneous cache sizes is established, subsuming prior results.
  • The centralized version of the bound is shown to relate to the generalized independence number bound in index coding.

Conclusions:

  • The proposed generic converse provides a unified framework for analyzing data exchange problems.
  • The derived bounds offer significant improvements, particularly for coded caching with heterogeneous cache sizes.
  • The work deepens the understanding of fundamental limits in distributed data exchange and coded communication systems.