Union bounds on the performance of product codes

We estimate the weight enumerator of a product code by using an exact expression for its known terms (e.g., the number of low weight words), and a binomial approximation for its unknown terms. We subsequently apply a union bound, using the estimated weight enumerator, to large product codes. The computed union bounds are similar to the simulation results of iterative (turbo) decoding of such codes as reported in literature.