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IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC)

Sum-product decoding for sparse quantum codes over random balanced X-Z channel

Han Chun-Lei, Yun-Jiang Wang, Sha Shi, Jing Yu

Published Sep 1, 2015• 0 citations
Publisher

Abstract

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.

DOI
10.1109/icspcc.2015.7338965

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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.
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.
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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.
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.
We address the problem of decoding sparse quantum error correction codes. For Pauli channels, this task can be accomplished by a version of the belief propagation algorithm used for decoding sparse classical codes. Quantum codes pose two new challenges however. Firstly, their Tanner graph unavoidably contain small loops which typically undermines the performance of belief propagation. Secondly, sparse quantum codes are by definition highly degenerate. The standard belief propagation algorithm does not exploit this feature, but rather it is impaired by it. We propose heuristic methods to improve belief propagation decoding, specifically targeted at these two problems. While our results exhibit a clear improvement due to the proposed heuristic methods, they also indicate that the main source of errors in the quantum coding scheme remains in the decoding.