An iterative algorithm for soft-input soft-output (SISO) decoding of classical algebraic cyclic block codes is presented below. Inspired by other approaches for high performance belief propagation (BP) decoding, this algorithm requires up to 10 times less computational complexity than other methods that achieve similar performance. By utilizing multiple BP decoders, and using random permutation taken from the permutation group of the code, this algorithm reaches near maximum likelihood performance. A computational complexity comparison of the proposed algorithm versus other methods is presented as well. This includes complexity versus performance analysis, allowing one to trade between the former and the latter, according to ones needs.