Abstract: A matrix transform method and circuit provides for MAP decoding of turbo codes. The method begins by initializing a forward recursion probability function vector &agr;0, and a backward recursion probability function vector &bgr;N. Then, transition probability matrices &Ggr;(Rk) and &Ggr;i(Rk) are determined according to each received symbol of the sequence R1N. And then, values of &agr;k, corresponding to the received Rk are determined according to &Ggr;(Rk). At the same time of determining &agr;k, a plurality of multiplacation on &Ggr;(Rk) and &Ggr;i(Rk) are accomplished in parallel. By making use of the results of the matrix multiplications, after receiving the complete symbol sequence R1N, values of all of the backward recursion probability vector &bgr;k, where k=1, 2, . . . , N−1, are determined in parallel, and the log likelihood ratio for every decoded bit dk, k=1, 2, . . . , N, are also determined in parallel.