Matrix approach for fast implementations of logarithmic MAP decoding of turbo codes

This paper describes two new matrix transform algorithms for the max-log-MAP decoding of turbo codes. In the proposed algorithms, the successive decoding procedures carried out in the conventional max-log-MAP algorithm are performed in parallel, and well formulated into a set of simple and regular matrix operations, which can therefore considerably speed up the decoding operations and reduce the computational complexity. The matrix max-log-MAP algorithms also maintain the advantage of the general logarithmic MAP like algorithms in avoiding complex numerical representation problems. They particularly facilitate the implementations of the logarithmic MAP like algorithms in special-purpose parallel processing VLSI hardware architectures. The matrix algorithms also allow simple implementations by using shift registers. The proposed implementation architectures for the matrix max-log-MAP decoding can effectively reduce the memory capacity and simplify the data accesses and transfers required by the conventional max-log-MAP as well as MAP algorithms