---
title: Deriving the Normalized Min-Sum Algorithm from Cooperative Optimization
url: https://www.emergentmind.com/papers/0609088
type: paper
arxiv_id: '0609088'
arxiv_url: https://arxiv.org/abs/0609088
published: '2006-09-15'
categories:
- cs.IT
- math.IT
---

# Deriving the Normalized Min-Sum Algorithm from Cooperative Optimization

## Abstract

The normalized min-sum algorithm can achieve near-optimal performance at decoding LDPC codes. However, it is a critical question to understand the mathematical principle underlying the algorithm. Traditionally, people thought that the normalized min-sum algorithm is a good approximation to the sum-product algorithm, the best known algorithm for decoding LDPC codes and Turbo codes. This paper offers an alternative approach to understand the normalized min-sum algorithm. The algorithm is derived directly from cooperative optimization, a newly discovered general method for global/combinatorial optimization. This approach provides us another theoretical basis for the algorithm and offers new insights on its power and limitation. It also gives us a general framework for designing new decoding algorithms.