Deriving the Normalized Min-Sum Algorithm from Cooperative Optimization

TL;DR

This paper derives the normalized min-sum decoding algorithm for LDPC codes from cooperative optimization, providing a new theoretical foundation and insights into its capabilities and limitations.

Contribution

It introduces a novel derivation of the normalized min-sum algorithm from cooperative optimization, offering a new theoretical perspective and framework for decoding algorithms.

Findings

Provides a new theoretical basis for the normalized min-sum algorithm

Offers insights into the algorithm's power and limitations

Establishes a framework for designing new decoding algorithms

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.