  We present an algorithm to construct quantum circuits for encoding and
inverse encoding of quantum convolutional codes. We show that any quantum
convolutional code contains a subcode of finite index which has a
non-catastrophic encoding circuit. Our work generalizes the conditions for
non-catastrophic encoders derived in a paper by Ollivier and Tillich
(quant-ph/0401134) which are applicable only for a restricted class of quantum
convolutional codes. We also show that the encoders and their inverses
constructed by our method naturally can be applied online, i.e., qubits can be
sent and received with constant delay.
