Generalized product accumulate codes: Analysis and performance

In [1] [2] , product accumulate (PA) codes were proposed and shown to be a class of simple and provably good codes for rate R greater than or equal to 1/2. This work investigates the generalized product accumulate (GPA) codes which have rates over the entire range and which are also "good" both in the maximum likelihood (ML) sense and under the iterative approach. Analysis concentrates on the weight distribution over the code ensemble, the ML bounds, and the existence and computation of threshold phenomenon in the iterative decoding. A tight upper bound due to Divsalar and the thresholds computed using density evolution are examined. Simulations are presented and evaluated, especially for rate R < 1/2.