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In this paper, we discuss the reduction of error-trellises for tail-bitingconvolutional codes. In the case where some column of a parity-check matrix hasa monomial factor (with indeterminate D), we show that the associatedtail-biting error-trellis can be reduced by cyclically shifting thecorresponding error-subsequence by l (the power of D) time units. We see thatthe resulting reduced error-trellis is again tail-biting. Moreover, we showthat reduction is also possible using backward-shifted error-subsequences.

Reduction of Error-Trellises for Tail-Biting Convolutional Codes Using Shifted Error-Subsequences