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 α0, and a backward recursion probability function vector βN. Then, transition probability matrices Γ(Rk) and Γi(Rk) are determined according to each received symbol of the sequence R1N. And then, values of αk, corresponding to the received Rk are determined according to Γ(Rk). At the same time of determining αk, a plurality of multiplacation on Γ(Rk) and Γi(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 βk, 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. 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.

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