MAP algorithms for decoding linear block codes based on sectionalized trellis diagrams

The MAP algorithm is a trellis-based maximum a posteriori probability decoding algorithm. It is the heart of the turbo decoding or iterative decoding which can achieve an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions cause long decoding delay. For practical applications, this decoding algorithm must be simplified and its decoding complexity and delay must be reduced. In this paper, the MAP and max-log-MAP algorithms are first applied to sectionalized trellises for linear block codes. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Also presented in this paper are bi-directional and parallel MAP decoding.