scholarly journals An improved belief propagation algorithm for detecting mesoscale structure in complex networks

2020 ◽  
Vol 30 (2) ◽  
pp. 023112
Author(s):  
Chuang Ma ◽  
Bing-Bing Xiang ◽  
Han-Shuang Chen ◽  
Hai-Feng Zhang
Keyword(s):  
Complex Networks ◽  
Belief Propagation ◽  
Mesoscale Structure ◽  
Propagation Algorithm ◽  
Belief Propagation Algorithm

On the iterative decoding of sparse quantum codes

2008 ◽  
Vol 8 (10) ◽  
pp. 986-1000
Author(s):  
D. Poulin ◽  
Y. Chung
Keyword(s):  
Iterative Decoding ◽  
Belief Propagation ◽  
Quantum Codes ◽  
Error Correction Codes ◽  
Heuristic Methods ◽  
Tanner Graph ◽  
Coding Scheme ◽  
Propagation Algorithm ◽  
Belief Propagation Algorithm ◽  
Quantum Error

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.

On the iterative decoding of sparse quantum codes

2008 ◽  
Vol 8 (10) ◽  
pp. 986-1000
Author(s):  
D. Poulin ◽  
Y. Chung
Keyword(s):  
Iterative Decoding ◽  
Belief Propagation ◽  
Quantum Codes ◽  
Error Correction Codes ◽  
Heuristic Methods ◽  
Tanner Graph ◽  
Coding Scheme ◽  
Propagation Algorithm ◽  
Belief Propagation Algorithm ◽  
Quantum Error

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.

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