$l_2$-Box ADMM Decoding for LDPC Codes Over ISI Channels

Abstract

The alternating direction method of multipliers (ADMM) has been adapted for decoding low-density parity-check (LDPC) codes over intersymbol interference (ISI) channels in order to reduce the complexity of the traditional Turbo equalization (TE) method. However, the error rate performance of ADMM decoding may be degraded in certain ISI channels when compared with the TE at high signal-to-noise ratio regions. In order to address the problem, we derive a novel ADMM-based decoding method, called l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -box ADMM decoding, for LDPC codes over ISI channels. By introducing suitable penalty functions to l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -box ADMM decoding, we present an enhanced method, called l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -box ADMM penalized decoding, to further improve the performance. Simulation results on several ISI channels indicate that the proposed l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -box ADMM penalized decoding can achieve better error rate performances compared with the TE and the existing ADMM penalized decoding methods, especially for ISI channels with long memory, while maintaining the low-complexity advantage of the ADMM penalized decoding.