Efficient QP-ADMM Decoder for Binary LDPC Codes and Its Performance Analysis

TL;DR

This paper introduces a novel QP-ADMM decoding algorithm for binary LDPC codes that reduces complexity and guarantees convergence, showing promising simulation results for decoding performance.

Contribution

It develops a non-convex quadratic programming decoder using ADMM that simplifies computations and proves convergence, advancing LDPC decoding methods.

Findings

Linear complexity per iteration in code length

Converges to a stationary point under certain conditions

Effective decoding demonstrated through simulations

Abstract

This paper presents an efficient quadratic programming (QP) decoder via the alternating direction method of multipliers (ADMM) technique, called QP-ADMM, for binary low-density parity-check (LDPC) codes. Its main contents are as follows: first, we relax maximum likelihood (ML) decoding problem to a non-convex quadratic program. Then, we develop an ADMM solving algorithm for the formulated non-convex QP decoding model. In the proposed QP-ADMM decoder, complex Euclidean projections onto the check polytope are eliminated and variables in each updated step can be solved analytically in parallel. Moreover, it is proved that the proposed ADMM algorithm converges to a stationary point of the non-convex QP problem under the assumption of sequence convergence. We also verify that the proposed decoder satisfies the favorable property of the all-zeros assumption. Furthermore, by exploiting the inside structures of the QP model, the complexity of the proposed algorithm in each iteration is shown to be linear in terms of LDPC code length. Simulation results demonstrate the effectiveness of the proposed QP-ADMM decoder.