Map decoding for turbo codes by parallel matrix processing

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; , and a backward recursion probability function vector &bgr; . Then, transition probability matrices &Ggr;(R ) and &Ggr; (R ) are determined according to each received symbol of the sequence R . And then, values of &agr; , corresponding to the received R are determined according to &Ggr;(R ). At the same time of determining &agr; , a plurality of multiplacation on &Ggr;(R ) and &Ggr; (R ) are accomplished in parallel. By making use of the results of the matrix multiplications, after receiving the complete symbol sequence R , values of all of the backward recursion probability vector &bgr; , where k=1, 2, . . . , N−1, are determined in parallel, and the log likelihood ratio for every decoded bit d , k=1, 2, . . . , N, are also determined in parallel. The circuit performs successive decoding procedures in parallel using a set of regular matrix operations. These operations substantially accelerate the decoding speed and reduce the computational complexity, and are particularly suited for implementation in special-purpose parallel processing VLSI hardware architectures. Using shift registers, the VLSI implementation effectively reduces memory requirements and simplifies complicated data accesses and transfers.