On the bit error probability for constant log-MAP decoding of convolutional codes

Maximum a posteriori probability (MAP) decoding minimizes the symbol or bit error probability, however, few studies have performed an exact error performance evaluation, although the optimality does not require explanation. The MAP algorithm is much more complex than maximum likelihood decoding methods, therefore, suboptimal MAP algorithms are considered for practical systems. The Max-Log-MAP decoding algorithm is one of several near optimum algorithms that reduce decoding complexity. However, it is shown that turbo decoding with Max-Log-MAP has an error-performance degradation compared with MAP decoding. Log-MAP decoding can be realized using Max-Log-MAP decoding with a correction term, which corrects the error induced by maximum approximation. Constant Log-MAP decoding employs the constant correction term instead of the log-domain correction term. In this paper, analytical results of bit error probability of convolutional codes with constant Log-MAP decoding are shown. Furthermore, the analytical results are compared with the result of Max-Log-MAP decoding, and the improvement by the correction term which correct error induced by maximum approximation is presented, theoretically. The results show that the error performance of constant Log-MAP decoding is slightly better than Max-Log-MAP decoding.