  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.
