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

• Published in: IEEE transactions on communications Vol. 48; no. 4; pp. 577 - 587
• Main Authors: Ye Liu, Shu Lin, Fossorier, M.P.C.
• Format: Journal Article
• Language: English
• Published: Goddard Space Flight Center IEEE 01.04.2000; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Block codes; Communications Society; Complexity; Computation; Computer Programming And Software; Convolutional codes; Decoding; Delay; Error correction; Error probability; Heart; Iterative algorithms; Iterative decoding; NASA; Optimization; Recursion
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/26.843125

The maximum a posterioriprobability (MAP) algorithm is a trellis-based MAP decoding algorithm. It is the heart of turbo (or iterative) decoding that achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in a long decoding delay. For practical applications, this decoding algorithm must be simplifled and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variation's, such as log-MAP and max-log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bidirectional and parallel MAP decodings.