ADMM decoding on trapping sets

Alternating direction method of multipliers (ADMM) decoding is a new decoding framework for low-density parity-check (LDPC) codes. It can be used to implement linear programming (LP) decoding or penalized LP decoding. Similar to belief propagation (BP) decoding, ADMM decoding consists of local “check” and “variable updates”. However, ADMM decoding performs better than BP at high signal-to-noise ratios (SNRs). To understand why these two locally operating algorithms result in different error floor behaviors, we study the dynamics of ADMM decoding in this paper. In particular, we focus on trapping sets, which are observed to cause error floors in ADMM decoding. Our results show that the dynamics of ADMM decoding on trapping sets can be characterized as a jump linear system. Furthermore, these results indicate that the Lagrange multipliers involved in ADMM play an important role in correcting trapping set errors. Finally, we present simulation results that support this understanding.