Minimal-memory, non-catastrophic, polynomial-depth quantum convolutional encoders
Abstract
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, non-catastrophic, 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 non-recursive. Finally, we apply our technique to many quantum convolutional codes from the literature.
Cite
@article{arxiv.1105.0649,
title = {Minimal-memory, non-catastrophic, polynomial-depth quantum convolutional encoders},
author = {Monireh Houshmand and Saied Hosseini-Khayat and Mark M. Wilde},
journal= {arXiv preprint arXiv:1105.0649},
year = {2013}
}
Comments
Continuation and expansion of arXiv:1011.5535; 21 pages, 2 figures; v2 includes an elementary proof that the encoders in this paper are non-recursive in addition to being non-catastrophic; v3, accepted into IEEE Transactions on Information Theory