Parameter-free ℓp\ell_p-Box Decoding of LDPC Codes

The Alternating Direction Method of Multipliers (ADMM) decoding of Low Density Parity Check (LDPC) codes has received many attentions due to its excellent performance at the error floor region. In this paper, we develop a parameter-free decoder based on Linear Program (LP) decoding by replacing the binary constraint with the intersection of a box and an $\ell_p$ sphere. An efficient $\ell_2$-box ADMM is designed to handle this model in a distributed fashion. Numerical experiments demonstrate that our decoder attains better adaptability to different Signal-to-Noise Ratio and channels

ADMM-based Decoder for Binary Linear Codes Aided by Deep Learning

Inspired by the recent advances in deep learning (DL), this work presents a deep neural network aided decoding algorithm for binary linear codes. Based on the concept of deep unfolding, we design a decoding network by unfolding the alternating direction method of multipliers (ADMM)-penalized decoder. In addition, we propose two improved versions of the proposed network. The first one transforms the penalty parameter into a set of iteration-dependent ones, and the second one adopts a specially designed penalty function, which is based on a piecewise linear function with adjustable slopes. Numerical results show that the resulting DL-aided decoders outperform the original ADMM-penalized decoder for various low density parity check (LDPC) codes with similar computational complexity.Comment: 5 pages, 4 figures, accepted for publication in IEEE communications letter

A PDD Decoder for Binary Linear Codes With Neural Check Polytope Projection

Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity and poor performance at the low signal-to-noise ratio (SNR) region. In this letter, we adopt the penalty dual decomposition (PDD) framework and propose a PDD algorithm to address the fundamental polytope based maximum likelihood (ML) decoding problem. Furthermore, we propose to integrate machine learning techniques into the most time-consuming part of the PDD decoding algorithm, i.e., check polytope projection (CPP). Inspired by the fact that a multi-layer perception (MLP) can theoretically approximate any nonlinear mapping function, we present a specially designed neural CPP (NCPP) algorithm to decrease the decoding latency. Simulation results demonstrate the effectiveness of the proposed algorithms.Comment: This pape has been accepted for publication in IEEE wireless communications letter

A Reduced-Complexity Projection Algorithm for ADMM-based LP Decoding

The Alternating Direction Method of Multipliers has recently been adapted for Linear Programming Decoding of Low-Density Parity-Check codes. The computation of the projection onto the parity polytope is the core of this algorithm and usually involves a sorting operation, which is the main effort of the projection. In this paper, we present an algorithm with low complexity to compute this projection. The algorithm relies on new findings in the recursive structure of the parity polytope and iteratively fixes selected components. It requires up to 37% less arithmetical operations compared to state-of-the-art projections. Additionally, it does not involve a sorting operation, which is needed in all exact state-of-the-art projection algorithms. These two benefits make it appealing for efficient hard- and software implementations