Turbo codes are preferred for high rate data services in the third generation mobile communication system IMT-2000.Thus low decoding delay and low complexity iterative decoding are of paramount importance.The modiffied soft output Viterbi algorithm(SOVA)and the Max-Log-MAP algorithm are such decoding techniques.The equivalence of the modified SOVA and Max-Log-MAP algorithm has been proven under the condition of no a priori information and infinite decoding depth.Since the a priori information has to be updated in iterative decoding

we prove their equivalence when there exists a priori information in the paper.We also discuss the relationship between the sliding window Max-Log-MAP algorithm and the modified SOVA for finite decoding depth.