Decoding LDPC Codes by Using Negative Proximal Regularization

Yiming Chen, Rui Wang, Jinglong Zhu, Zaiwen Wen

Abstract:

The low-density parity-check (LDPC) decoding
problem can be expressed as an integer linear programming
(ILP) problem. One efficient method to solve the ILP problem
is to relax the integer constraints and add penalty terms to the
objective function, and the revised problem can be solved via the
alternating direction method of multipliers (ADMM) algorithm.
These penalty terms can punish the non-integral solutions and
improve the decoding performance of the decoder. However,
ADMM decoders are easily trapped in a local solution, which
limits the frame error rate (FER) performance of the decoders
at low signal-to-noise ratios (SNR). In this paper, we propose
a restartable ADMM-based decoder using a negative proximal
regularization. The negative proximal term will be updated
whenever the decoder finds a new local solution. Therefore,
the decoder can be restarted several times and the candidate
solution which satisfies the parity-check equations and has the
lowest objective function value can be selected as the decoder’s
output. Some properties, together with several choices of penalty
terms are discussed. We also investigate the convergence of our
proposed decoder, and prove that the possibility of decoding
errors is independent of the codeword that is transmitted.
Simulation results show that our proposed decoder outperforms
other ADMM-based decoders in most cases, while the decoding
complexity maintains the same.