one path 84 the accumulated probabilities are compared and selected the u with larger probability the soft decision are made based on the final probability selected for each bit fig1 a shows the implementation for calculating the posteriori probability for u 0 fig1 b shows the implementation for calculate the posteriori probability for u 1 fig1 shows the implementation of compare and select the u with larger probability fig1 shows the implementation of the soft decode compare logic to produce output bits based on the posteriori probability of u 0 and u 1 the equations for calculation the accumulated probabilities for each state and compare and select are shown below sum u2014 s 00 sm 0 i bm 1 sm 0 j sum u2014 s 01 sm 3 i bm 7 sm 1 j sum u2014 s 02 sm 4 i bm 9 sm 2 j sum u2014 s 03 sm 7 i bm 15 sm 3 j sum u2014 s 04 sm 1 i bm 4 sm 4 j sum u2014 s 05 sm 2 i bm 6 sm 5 j sum u2014 s 06 sm 5 i bm 12 sm 6 j sum u2014 s 07 sm 6 i bm 14 sm 7 j sum u2014 s 10 sm 1 i bm 3 sm 0 j sum u2014 s 11 sm 2 i bm 5 sm 1 j sum u2014 s 12 sm 5 i bm 11 sm 2 j sum.