Linear-Complexity ADMM Updates for Decoding LDPC Codes in Partial Response Channels

This letter investigates the application of alternating direction method of multipliers (ADMM) in decoding low-density parity-check (LDPC) codes over partial response (PR) channels. Unlike the ADMM decoding in memoryless channels, the ADMM decoding in PR channels becomes involved with the correlation among adjacent code symbols. As the update equations for code symbols constitute the most complicated part of the ADMM decoding in PR channels, this letter focuses on their derivation by making use of the iterative fashion of ADMM and incorporating the use of a penalty function. A notable advantage of the proposed ADMM penalized decoding algorithm is that its complexity increases linearly with the memory length of PR channels. Simulation results show that the proposed algorithm can achieve error performance comparable with that of Turbo equalization (TE) in the waterfall region. It can also outperform TE at high signal-to-noise ratios as iteration grows.