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Encoding and Decoding of CSS-Type Quantum Convolution Codes

Linrang Zhang

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The polynomial representation of a quantum state is defined.Based on the Calderbank-Shor-Steane(CSS)-type construction of quantum codes,a new method for encoding and decoding of CSS-type quantum convolution codes is presented.Its corresponding networks are also described.The basis state of the code is transformed into the multiplication of an information polynomial by the generator polynomial.Then networks can be realized with operations of polynomial multiplication. The simple method possesses a highly regular structure,and the networks are easy to realize.

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The polynomial representation of a quantum state is defined.Based on the Calderbank-Shor-Steane(CSS)-type construction of quantum codes,a new method for encoding and decoding of CSS-type quantum convolution codes is presented.Its corresponding networks are also described.The basis state of the code is transformed into the multiplication of an information polynomial by the generator polynomial.Then networks can be realized with operations of polynomial multiplication. The simple method possesses a highly regular structure,and the networks are easy to realize.
The research on quantum convolutional codes is aimed at protecting a flow of information over long distance communications. The polynomial representation of a quantum state is defined. Based on the Calderbank-Shor-Steane(CSS)-type construction of quantum codes, a new method for encoding and decoding of CSS-type quantum convolutional codes is presented and corresponding networks are described. The basis state of the code is transformed into the product of an information polynomial by the generator polynomial. Then networks can be realized by operations of polynomial multiplication. Finally, inspired by classical convolutional decoding idea, a quantum Viterbi algorithm with linear complexity is put forward.
A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in the Shannon-theoretic sense and that are decodable in polynomial time are presented. The rate is the highest among those known to be achievable by CSS codes. Moreover, the best known lower bound on the greatest minimum distance of codes constructible in polynomial time is improved for a wide range.
Quantum communication system is influenced by environment noise in the whole process. Quantum error-correcting codes can solve this problem efficiently. The polynomial representation of a quantum state is defined. Based on the structure of the classical convolutional codes, the basis state of the quantum convolutional codes is transformed into the multiplication of an information polynomial by the generator polynomial. A new method is proposed to encode and decode these quantum codes and the networks can be realized with the polynomial multiplication circuits. Finally, we provide a maximum likelihood error estimation algorithm with complexity growing linearly.
A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in the Shannon theoretic sense and that are decodable in polynomial time are presented. The rate is the highest among those known to be achievable by CSS codes. Moreover, the best known lower bound on the greatest minimum distance of codes constructible in polynomial time is improved for a wide range.
A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum error-correcting code. It is known that conjugate code pairs are applicable to quantum cryptography. In this work, a polynomial construction of conjugate code pairs is presented. The constructed pairs achieve the highest known achievable rate on additive channels, and are decodable with algorithms of polynomial complexity.