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Convolutional and tail-biting quantum error-correcting codes

G. David Forney, Jr.·Markus Grassl·Saikat Guha
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Abstract

Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to 4096 states and minimum distances up to 10 are constructed as stabilizer codes from classical self-orthogonal rate-1/n F_4-linear and binary linear convolutional codes, respectively. These codes generally have higher rate and less decoding complexity than comparable quantum block codes or previous quantum convolutional codes. Rate-(n-2)/n block stabilizer codes with the same rate and error-correction capability and essentially the same decoding algorithms are derived from these convolutional codes via tail-biting.

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G. David Forney, Jr., Markus Grassl, Saikat Guha. 2006-11-07. Convolutional and tail-biting quantum error-correcting codes. https://doi.org/10.1109/tit.2006.890698

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