Ordered Binary Decision Diagrams and Minimal Trellises
IEEE Transactions on Computers
A Posteriory Probability Decoding of Nonsystematically Encoded Block Codes
Problems of Information Transmission
On Viterbi-like algorithms and their application to Reed-Muller codes
Journal of Complexity - Special issue on coding and cryptography
Complexity Reduction in SISO Decoding of Block Codes
Wireless Personal Communications: An International Journal
New constructions of high-performance low-complexity convolutional codes
IEEE Transactions on Communications
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While the complexity of trellis decoding for a given block code is essentially a function of the number of states and branches in its trellis, the decoding complexity may be often reduced by means of an appropriate sectionalization of the trellis. Notwithstanding the many examples of such sectionalizations for particular codes that appeared in the literature, no systematic method for finding the best sectionalization of a given trellis is presently known. We present a polynomial-time algorithm which produces the optimal sectionalization of a given trellis T in time O(n2), where n is the length of the code generated by T. The algorithm is developed in a general setting of certain operations and functions defined on the set of trellises; it therefore applies to both linear and nonlinear codes, and easily accommodates a broad range of optimality criteria. The particular optimality criterion based on minimizing the total number of additions and comparisons required for maximum-likelihood trellis decoding is investigated in detail: several different methods for decoding a given trellis are discussed and compared in a number of examples. Finally, analysis of the dynamical properties of certain optimal sectionalizations is presented