On the complexity of turbo decoding algorithms

We evaluate the computational complexity of several turbo decoding algorithms: log maximum a posteriori (log-MAP), maximum log-MAP (max-log-MAP) and the soft output Viterbi (see IEEE Journal on Selected Areas in Communications, vol.16, no.2, p.260-64,1998) algorithm (SOVA). The computational complexity is analyzed in terms of mathematical operations and the results are normalized by an equivalent addition operation for easy comparison. Furthermore, these algorithms are programmed on a DSP and the number of CPU cycles per decoded bit is measured. Our approach leads to a quick complexity estimate of a turbo decoder with respect to the conventional Viterbi decoder. Both analyzed and measured results suggest that the max-log-MAP algorithm is the best implementation choice because it is the least complex and exhibits only minor performance loss.