Improved Free-of-CPP ADMM-Based Iterative Decoding Algorithm of Binary LDPC Codes

doi:10.1109/LSP.2024.3511336

Improved Free-of-CPP ADMM-Based Iterative Decoding Algorithm of Binary LDPC Codes

2025-01-01

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DOI：10.1109/LSP.2024.3511336

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Iterative decoding algorithms based on the alternating direction method of multipliers (ADMM) decoding of low density parity check (LDPC) codes has emerged as an alternating decoding method and bringed a boom of research on drawing upon mathematical optimization to LDPC decoding. Improving error-correcting performance is a key issue to enhance the superiority of ADMM decoding. In this letter, we investigate an efficient ADMM-based iterative decoder for binary LDPC codes. First, we build an mathematical programming equivalence of the maximum likelihood (ML) decoding problem by transforming parity-check constraints to multiple equivalent linear constraints and eliminating check-polytope projection (CPP). Then, an iterative algorithm based on ADMM technique is developed to solve this free-of-CPP (FCPP) equivalence and each ADMM update can be computed efficiently. Moreover, the proposed ADMM-FCPP decoding algorithm is analyzed to display a linear complexity to the length of the LDPC code at each iteration. Finally, simulation results demonstrate the superiority of the proposed decoder in error-correcting performance compared with the state-of-the-art ADMM-based decoders.

Keywords:

Maximum likelihood decoding

Iterative decoding

Convex functions

Vectors

Signal processing algorithms

Optimization

Complexity theory

Simulation

Programming profession

Low-density parity-check (LDPC) codes

alternating direction method of multipliers (ADMM)

check- polytope projection (CPP)

mathematical programming

Improved Free-of-CPP ADMM-Based Iterative Decoding Algorithm of Binary LDPC Codes

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