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Finite-Length Analyses for Source and Channel Coding on Markov Chains.

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Summary
This summary is machine-generated.

This study develops finite-length bounds for Markov chain source and channel coding. The derived bounds are computationally efficient and asymptotically optimal, advancing information theory for practical applications.

Keywords:
Markov chainchannel codingfinite-length analysissource coding

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Area of Science:

  • Information Theory
  • Coding Theory
  • Probability and Statistics

Background:

  • Markov chains are fundamental in modeling sequential data.
  • Finite-length analysis is crucial for practical coding systems.
  • Existing bounds often lack computational efficiency or asymptotic tightness.

Purpose of the Study:

  • Derive finite-length bounds for source coding with side-information and channel coding with Markovian noise.
  • Ensure these bounds are asymptotically tight and efficiently computable.
  • Establish theoretical performance limits for these coding problems.

Main Methods:

  • Utilized large deviation, moderate deviation, and second-order bounds.
  • Introduced novel information measures for transition matrices.
  • Developed low computational complexity upper and lower bounds for coding length.

Main Results:

  • Established finite-length upper and lower bounds for the two coding problems.
  • Demonstrated asymptotic optimality of the derived bounds.
  • Showcased efficient computability of the bounds.

Conclusions:

  • The derived finite-length bounds offer a practical and theoretically sound approach to source and channel coding with Markov chains.
  • These bounds provide a more accurate performance assessment than asymptotic results alone.
  • The work contributes to the advancement of efficient and optimal coding schemes in information theory.