Non-catastrophic Encoders and Encoder Inverses for Quantum Convolutional Codes

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 Oliver and Tillich (quant-ph/0401134) which are applicable only for a restricted class of quantum convolutional codes We also show that the encodes and their inverse constructed by our method naturally can be applied online, i.e., qubits can be sent and received with constant delay