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Low-Complexity Automorphism Ensemble Decoding of Reed-Muller Codes Using Path Pruning.

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  • 1School of Electronic and Information Engineering, Beihang University, Beijing 100191, China.

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Summary
This summary is machine-generated.

We developed a new method to reduce the complexity of the automorphism ensemble decoder (AED) for Reed-Muller (RM) codes. This technique significantly cuts down computational cost without sacrificing decoding performance.

Keywords:
Plotkin constructionReed–Muller (RM) codesautomorphism ensemble decodingcomplexity reduction

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Area of Science:

  • Coding Theory
  • Information Theory
  • Digital Communications

Background:

  • Automorphism Ensemble Decoder (AED) offers near Maximum Likelihood (ML) performance for Reed-Muller (RM) codes.
  • High computational complexity limits AED's practical application due to exponential growth in ensemble size with code length.

Purpose of the Study:

  • To reduce the complexity of the AED for RM codes.
  • To maintain near ML performance while decreasing computational cost.

Main Methods:

  • Utilized the factor graph permutation group (FGPG), a subgroup of RM code automorphisms, for AED permutations.
  • Exploited permutation invariance (PI) and subcode estimate convergence (SEC) phenomena.
  • Implemented SEC-aided path pruning to reduce decoding complexity.

Main Results:

  • Proposed a uniform partitioning of FGPG based on affine bijection permutation matrices.
  • Demonstrated SEC phenomenon in AED using successive cancellation (SC) or SC list (SCL) decoders.
  • Achieved up to 67.6% complexity reduction with negligible performance degradation for short RM codes.

Conclusions:

  • SEC-aided path pruning effectively reduces AED complexity for RM codes.
  • The proposed method offers a practical solution for high-performance decoding of RM codes.