Quasi-Optimal Path Convergence-Aided Automorphism Ensemble Decoding of Reed-Muller Codes

Area of Science:

• Coding Theory
• Information Theory
• Digital Communications

Background:

• Automorphism Ensemble (AE) Successive Cancellation (SC) decoders offer near-maximum-likelihood (ML) performance for Reed-Muller (RM) codes.
• The high decoding complexity of AE-SC decoders stems from the need for multiple decoding attempts to achieve diversity gain.

Purpose of the Study:

• To propose a novel quasi-optimal path convergence (QOPC)-aided early termination (ET) technique for AE-SC decoding.
• To reduce the computational complexity of AE-SC decoding without significant performance degradation.

Main Methods:

• Developed a QOPC technique to detect convergence of partial path metrics (PPMs) in SC constituent decoders.
• Implemented an early termination strategy based on the QOPC criterion to prune non-optimal decoding paths.
• Evaluated performance and complexity reduction in both fully and partially parallel AE-SC decoding frameworks.

Main Results:

• The QOPC-aided ET method achieved negligible performance loss for medium-to-high-rate RM codes in the short-length regime.
• Complexity reduction ranged from 35.9% to 47.4% at a block error rate (BLER) of 10-3, outperforming existing methods.
• Under a partially parallel framework, complexity reduction reached 81.3% to 86.7% at a BLER of 10-5, maintaining near-ML performance.

Conclusions:

• The proposed QOPC-aided ET technique effectively reduces AE-SC decoding complexity for RM codes.
• This method offers a practical solution for improving the efficiency of high-performance decoders.
• The technique demonstrates superior performance and complexity reduction compared to state-of-the-art methods.