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Bhattacharyya Parameter of Monomial Codes for the Binary Erasure Channel: From Pointwise to Average Reliability
Vlad-Florin Drăgoi1,2, Gabriela Cristescu1
1Faculty of Exact Sciences, Aurel Vlaicu University of Arad, 2 Elena Dragoi Street, 310130 Arad, Romania.
Researchers refined order relations for polar codes on binary erasure channels. New methods using network theory minimize average error probability, improving code construction and reliability analysis.
Area of Science:
- Coding Theory
- Information Theory
- Network Theory
Background:
- Monomial codes utilize partial order relations for structural insights and efficient polar code construction.
- Existing order relations for polar codes on binary erasure channels are being refined.
Purpose of the Study:
- To refine existing order relations for polar codes specifically for the binary erasure channel.
- To investigate the application of average reliability from network theory to polar codes.
- To develop codes that minimize average error probability instead of just error probability.
Main Methods:
- Refining existing partial order relations for binary erasure channels.
- Applying concepts from reliability network theory to polar coding.
- Minimizing the average error probability of synthetic channels for polar codes.
Main Results:
- A new order relation is established, approximating the ultimate order relation based on the Bhattacharyya parameter.
- The concept of average reliability is successfully applied to polar codes for the binary erasure channel.
- A closed-form formula for the average reliability of specific synthetic channels is derived.
Conclusions:
- The refined order relations and average reliability approach offer improved methods for constructing and analyzing polar codes.
- This work bridges network theory and coding theory, providing practical tools for error correction.
- The derived formula aids in understanding and optimizing polar code performance on binary erasure channels.
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