Real-time algorithms and VLSI architectures for soft output MAP convolutional decoding

Soft output decoding algorithms have been attracting considerable attention for concatenated or iterative decoding systems. The most prominent is the soft output Viterbi algorithm (SOVA), which can be regarded as an approximation to the optimum symbol by symbol detector, the symbol by symbol MAP algorithm. The MAP algorithm is a block detector, i.e. it requires completed reception of a terminated block of received symbols, which prevents an efficient real-time implementation. Therefore, up to now, the SOVA was considered to be the more attractive alternative. In this paper, we first introduce an algebraic formulation for the MAP. Using this formulation, a novel real-time MAP algorithm (SMAP) is derived, and it is proved that in terms of hard decoding performance, the SMAP is equivalent to the VA with path memory truncation and best state decoding. The finally presented SMAP architectures provide a competitive alternative to the known SOVA architectures for soft output decoding applications