Simple Rate-1/3 Convolutional and Tail-Biting Quantum Error-Correcting Codes

Abstract

Simple rate-1/3 single-error-correcting unrestricted and CSS-type quantum convolutional codes are constructed from classical self-orthogonal $\F_4$-linear and $\F_2$-linear convolutional codes, respectively. These quantum convolutional codes have higher rate than comparable quantum block codes or previous quantum convolutional codes, and are simple to decode. A block single-error-correcting [9, 3, 3] tail-biting code is derived from the unrestricted convolutional code, and similarly a [15, 5, 3] CSS-type block code from the CSS-type convolutional code.

5 pages; to appear in Proceedings of 2005 IEEE International Symposium on Information Theory

References in corpus (3)

• Sparse Graph Codes for Quantum Error-Correction
• Description of a quantum convolutional code
• Quantum convolutional codes: fundamentals

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• Quantum Convolutional Coding with Shared Entanglement: General Structure
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• On Quantum and Classical Error Control Codes: Constructions and Applications
• Examples of minimal-memory, non-catastrophic quantum convolutional encoders
• A Review of Procedure to Evolve Quantum Procedures