Error-trellises for tailbiting convolutional codes

In this paper, we present an error-trellis construction for tailbiting convolutional codes. A tailbiting error-trellis is characterized by the condition that the syndrome former starts and ends in the same state. We clarify the correspondence between code subtrellises in the tailbiting code-trellis and error subtrellises in the tailbiting error-trellis. Also, we obtain the scalar parity-check matrix for a tailbiting convolutional code. Moreover, we show the close relationship between code-trellises for an SST Viterbi decoder and error-trellises for a syndrome decoder. The proposed construction is based on the adjoint-obvious realization of a syndrome former.