State-complexity reduction for convolutional codes using trellis-modlule integration
Assume that G(D) is a k(0) x n(0) canonical generator matrix. Let G((L))(D) be the generator matrix obtained by integrating L consecutive trellis-modules associated with G(D). We also consider a modified version of G((L))(D) using a column permutation. Then take notice of the corresponding minimal trellis-module T-(L). In this paper, we show that there is a case where the minimum number of states over all levels in T-(L) is less than the minimum attained for the minimal trellis-module associated with G(D). In this case, combining with a shifted sectionalization of the trellis, we can construct a trellis-module with further reduced number of states. We actually present such an example. We also clarify the mechanism of state-space reduction. That is, we show that trellis-module integration combined with an appropriate column permutation and a shifted sectionalization of the trellis is equivalent to shifting some particular bits of the original code bits by L time units.
convolutional codes trellis-module integration code trellis minimal trellis trellis complexity