An Analysis of the Block Error Probability Performance of Iterative Decoding

Asymptotic iterative decoding performance is analyzed for several classes of iteratively decodable codes when the block length of the codes N and the number of iterations I go to infinity. Three classes of codes are considered. These are Gallager's regular low-density parity-check (LDPC) codes, Tanner's generalized LDPC (GLDPC) codes, and the turbo codes due to Berrou It is proved that there exist codes in these classes and iterative decoding algorithms for these codes for which not only the bit error probability Pb, but also the block (frame) error probability P B, goes to zero as N and I go to infinity