Modification of the MAP algorithm for memory savings

It is usually assumed that all state metric values are necessary in the maximum a posteriori (MAP) algorithm in order to compute the a posteriori probability (APP) values. This paper extends the mathematical derivation of the original MAP algorithm and shows that the log likelihood values can be computed using only partial state metric values. By processing N stages in a trellis concurrently, the proposed algorithm results in savings in the required memory size and leads to a power efficient implementation of the MAP algorithm in channel decoding. The computational complexity analysis for the proposed algorithm is presented. Especially for the N = 2 case, we show that the proposed algorithm halves the memory requirement without increasing the compuational complexity.