Minimal-Memory, Noncatastrophic, Polynomial-Depth Quantum Convolutional Encoders

作者：Houshmand Monireh^*; Hosseini Khayat Saied; Wilde Mark M

来源：IEEE Transactions on Information Theory, 2013, 59(2): 1198-1210.

DOI：10.1109/TIT.2012.2220520

• Catastrophicity
• memory commutativity matrix
• minimal memory
• quantum convolutional codes

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.

• 出版日期2013-2