  We consider the decoding of convolutional codes using an error trellis
constructed based on a submatrix of a given check matrix. In the proposed
method, the syndrome-subsequence computed using the remaining submatrix is
utilized as auxiliary information for decoding. Then the ML error path is
correctly decoded using the degenerate error trellis. We also show that the
decoding complexity of the proposed method is basically identical with that of
the conventional one based on the original error trellis. Next, we apply the
method to check matrices with monomial entries proposed by Tanner et al. By
choosing any row of the check matrix as the submatrix for error-trellis
construction, a 1-state error trellis is obtained. Noting the fact that a
likelihood-concentration on the all-zero state and the states with many 0's
occurs in the error trellis, we present a simplified decoding method based on a
1-state error trellis, from which decoding-complexity reduction is realized.
