Physics – Quantum Physics
Scientific paper
2010-11-25
Proceedings of the International Symposium on Information Theory 2011 (ISIT 2011), pp. 450--454, St. Petersburg, Russia
Physics
Quantum Physics
5 pages, 2 figures, Accepted for the International Symposium on Information Theory 2011 (ISIT 2011), St. Petersburg, Russia; v
Scientific paper
10.1109/ISIT.2011.6034166
One of the most important open questions in the theory of quantum convolutional coding is to determine a minimal-memory, non-catastrophic, polynomial-depth convolutional encoder for an arbitrary quantum convolutional code. Here, we present a technique that finds quantum convolutional encoders with such desirable properties for several example quantum convolutional codes (an exposition of our technique in full generality will appear elsewhere). We first show how to encode the well-studied Forney-Grassl-Guha (FGG) code with an encoder that exploits just one memory qubit (the former Grassl-Roetteler encoder requires 15 memory qubits). We then show how our technique can find an online decoder corresponding to this encoder, and we also detail the operation of our technique on a different example of a quantum convolutional code. Finally, the reduction in memory for the FGG encoder makes it feasible to simulate the performance of a quantum turbo code employing it, and we present the results of such simulations.
Hosseini-Khayat Saied
Houshmand Monireh
Wilde Mark M.
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