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

## TL;DR

This paper introduces a low-complexity projection algorithm for ADMM-based LP decoding of LDPC codes, significantly reducing computational effort by eliminating sorting and leveraging recursive parity polytope structure.

## Contribution

It presents a novel projection algorithm that avoids sorting and reduces arithmetic operations by up to 37%, enhancing efficiency for LP decoding.

## Key findings

- Requires up to 37% fewer arithmetic operations
- Eliminates the need for sorting in projection computations
- Leverages recursive structure of the parity polytope

## Abstract

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.