Reduction of Error-Trellises for Tail-Biting Convolutional Codes Using   Shifted Error-Subsequences
  In this paper, we discuss the reduction of error-trellises for tail-biting convolutional codes. In the case where some column of a parity-check matrix has a monomial factor (with indeterminate D), we show that the associated tail-biting error-trellis can be reduced by cyclically shifting the corresponding error-subsequence by l (the power of D) time units. We see that the resulting reduced error-trellis is again tail-biting. Moreover, we show that reduction is also possible using backward-shifted error-subsequences. 
Masato Tajima, Koji Okino, and Tatsuto Murayama
cs.IT math.IT