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Acta Physica Sinica

Feedback iterative decoding of sparse quantum codes

Yun-Jiang Wang, Bai Bao-Ming, Xinmei Wang

Published Jan 1, 2010• 2 citations
Publisher

Abstract

Decoding sparse quantum codes can be accomplished by syndrome-based decoding through using the sum-product algorithm (SPA). We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard SPA. In our feedback strategy, we exploit not only the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model. Consequently, our decoding algorithm, on the one hand, can break the symmetric degeneracy, and on the other hand, can feed back more useful information to the SPA decoder to help the decoder determine a valid output, thereby significantly improving the decoding ability of the decoder. Moreover, our algorithm does not increase the measurement complexity compared with the previous method, but takes full advantage of the measured information.

DOI
10.7498/aps.59.7591

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Decoding sparse quantum codes can be accomplished by syndrome-based decoding through using the sum-product algorithm (SPA). We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard SPA. In our feedback strategy, we exploit not only the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model. Consequently, our decoding algorithm, on the one hand, can break the symmetric degeneracy, and on the other hand, can feed back more useful information to the SPA decoder to help the decoder determine a valid output, thereby significantly improving the decoding ability of the decoder. Moreover, our algorithm does not increase the measurement complexity compared with the previous method, but takes full advantage of the measured information.
Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm. We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP algorithm. In our feedback procedure, we exploit much of the information from stabilizers, not just the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model. Furthermore we show that our decoding algorithm is superior to belief propagation algorithms using only the syndrome in the feedback procedure for all cases of the depolarizing channel. Our algorithm does not increase the measurement overhead compared to the previous method, as the extra information comes for free from the requisite stabilizer measurements.
In this paper, a feedback sum-product decoding algorithm of sparse quantum codes for X-Z Pauli channels is developed. Compared with the previous decoding algorithm, our feedback strategy exploits not just the syndrome but also the values of the frustrated checks on individual qubits of the code and the character of the channel model with the portion of each error to adjust the probability distribution of information nodes. Due to the smart adjustment, our decoding algorithm, on one hand, can break the symmetric degeneracy, and on the other hand, can feed back more useful information to the SPA decoder to help the decoder determine a valid output, thereby significantly improving the decoding ability of the decoder. Moreover, our algorithm, which is based on GF(4), overcomes the limitation caused by decoding in GF(2). Finally, we want to point out that, our method does not increase the measurement overhead in comparison wioth the previous methods, as the extra information comes for free from the requisite stabilizer measurement.
Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm. We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP algorithm. In our feedback procedure, we exploit much of the information from stabilizers, not just the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model. Furthermore we show that our decoding algorithm is superior to belief propagation algorithms using only the syndrome in the feedback procedure for all cases of the depolarizing channel. Our algorithm does not increase the measurement overhead compared to the previous method, as the extra information comes for free from the requisite stabilizer measurements.
In this paper, we generalize the feedback sum-product algorithm to the decoding of sparse quantum codes over random balanced X-Z Channels, thereby significantly improving the performance of the concerned sparse quantum codes. We point out that, due to the randomness of the channel, degeneracy errors would be degreased greatly and the improvement of the performance of the sparse quantum codes come from the new decoding algorithm, where more reliable and useful information is feedback to the decoder by using the feedback strategy. As the end of this paper, simulations are given to verify our statements.
For quantum LDPC codes widely studied recent years,the decoding strategy based on the feedback sum-product( FSPA) we proposed before is investigated for the case of unbalanced X-Z channel. And the analysis of the corresponding performance of the FSPA is given. The study shows that under the unbalanced X-Z channel model, the feedback strategy could still exploit the syndrome comparison,the error style of the frustrated checks,the channel character analysis to adjust the probabilities distributions of the concerned information bits,thereby significantly improving the decoding ability of the sum-product decoder. Finally,simulation results verified our statements.
We present in this paper a new method for improving the decoding of the LDPC (low-density parity check) codes by optimising the log-SPA (sum-product algorithm). Currently, the LDPC codes give very good results with iterative decoding algorithm, log-SPA, based on the propagation confidence BP (belief propagation). To improve the existing log-SPA, we propose a decoding algorithm (log-SPA modified), which minimises the error decoding of words that could not be previously decoded. This algorithm is based on the dependency between the weight of the syndrome and the weight of the error sequence generated during iterations of decoding. Simulations illustrate the performance of our approach compared with classical LDPC code based on log-SPA.