Code/Error-Trellis Construction for Convolutional Codes Using Shifted Code/Error-Subsequences

摘要

In this paper, we present a code/error-trellis construction for convolutional codes using shifted code/error-subsequences. It is shown that if the identical shifts occur both in the subsequences of a code-path and in those of the corresponding error-path, then the code and error-trellises are reduced simultaneously, if reduction is possible. First, we obtain pairs of transformations which generate the identical shifts both in the subsequences of the code-path and in those of the error-path. Next, by applying these transformations to the generator matrix and the parity-check matrix, we show that the two associated trellises are reduced simultaneously.