Summary: In this paper, important methods for cryptanalysis of the stream cipher based on a class of keystream generators are discussed. These methods employ an approach called the fast correlation attack. This cryptographic problem is treated by considering its equivalent channel coding approach, namely decoding of certain very low rate codes in presence of very high noise. A novel family of algorithms for the fast correlation attack is presented. The algorithms are based on the iterative decoding principle in conjunction with a novel method for constructing the parity-checks. A goal of this paper is to summarize reported results and to compare some of the recent ones. Accordingly, the family is compared with recently proposed improved fast correlation attacks based on iterative decoding methods. An analysis of the algorithms performances and complexities is presented. The corresponding trade-offs between performance, complexity and required inputs are pointed out.