On trellis complexity of block codes: optimal sectionalizations

Every linear block code may be represented by a trellis, which can be employed for maximum likelihood decoding of the code with the Viterbi algorithm or variants thereof. We present a polynomial-time algorithm which produces the optimal sectionalization of a given trellis T for a block code C in time O(n²), where n is the length of C. 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 accommodates a broad range of optimality criteria. The optimality criterion based on minimizing the number of operations required for trellis decoding of C is investigated in detail. Several methods for decoding a given trellis are discussed and compared in a number of examples. An analysis of the dynamical properties of optimal sectionalizations is also presented