Low-Density Parity-Check Decoding Algorithm Based on Symmetric Alternating Direction Method of Multipliers

Area of Science:

• Coding Theory
• Signal Processing
• Information Theory

Background:

• Linear programming (LP) decoding of low-density parity-check (LDPC) codes is crucial for reliable communication.
• Conventional Alternating Direction Method of Multipliers (ADMM) offers efficiency but can struggle with non-integral solutions.
• Penalty terms in ADMM-based decoding improve frame error rate (FER) performance, particularly at low signal-to-noise ratios (SNRs).

Purpose of the Study:

• To derive explicit iterative steps for LP decoding of LDPC codes using the ADMM framework with penalty functions.
• To propose a novel Symmetric ADMM (S-ADMM) algorithm for enhanced LDPC code decoding efficiency and accuracy.
• To analyze the contraction properties of the proposed S-ADMM iterative sequence.

Main Methods:

• Leveraging the ADMM framework to develop iterative decoding steps for LDPC codes.
• Introducing penalty functions into the LP decoding objective function.
• Developing and implementing the Symmetric ADMM (S-ADMM) algorithm.
• Conducting simulation experiments to evaluate decoder performance.

Main Results:

• The proposed S-ADMM algorithm effectively solves the LP decoding problem for LDPC codes.
• S-ADMM demonstrates improved decoding efficiency and accuracy compared to conventional methods.
• Simulation results confirm superior performance of S-ADMM over standard ADMM penalized decoders across various LDPC and 5G codes.

Conclusions:

• The S-ADMM decoder offers significant improvements in decoding performance for LDPC codes.
• The proposed method is particularly effective in low SNR regions.
• S-ADMM represents a promising advancement for efficient and accurate LDPC code decoding in modern communication systems.