Quantum convolutional coding is a technique for encoding a stream of quantum information before transmitting it over a noisy quantum channel. Two important goals in the design of quantum convolutional encoders are to minimize the memory required by them and to avoid the catastrophic propagation of errors. In a previous paper, we determined minimal-memory, noncatastrophic, polynomial-depth encoders for a few exemplary quantum convolutional codes. In this paper, we elucidate a general technique for finding an encoder of an arbitrary quantum convolutional code such that the encoder possesses these desirable properties. We also provide an elementary proof that these encoders are nonrecursive. Finally, we apply our technique to many quantum convolutional codes from the literature. © 1963-2012 IEEE.
Publication Source (Journal or Book title)
IEEE Transactions on Information Theory
Houshmand, M., Hosseini-Khayat, S., & Wilde, M. (2013). Minimal-memory, noncatastrophic, polynomial-depth quantum convolutional encoders. IEEE Transactions on Information Theory, 59 (2), 1198-1210. https://doi.org/10.1109/TIT.2012.2220520