Quantum computation and quantum information
Quantum computation and quantum information
Convolutional factor graphs as probabilistic models
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Modern Coding Theory
Quantum error correction via codes over GF(4)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Codes on graphs: normal realizations
IEEE Transactions on Information Theory
A recursive approach to low complexity codes
IEEE Transactions on Information Theory
Sparse-graph codes for quantum error correction
IEEE Transactions on Information Theory
On factor graphs and the Fourier transform
IEEE Transactions on Information Theory
IEEE Communications Magazine
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A novel, practical and convenient approach to constructing Calderbank-Shor-Steane (CSS) codes based on factor graphs is presented in this paper. Our proposed method is applied to solve two problems associated with constructing CCS codes. One is judging whether a code is a weakly self-dual code or not, the other is finding the generator matrix and parity-check matrix of a weakly self-dual code. The novelty, practicality and convenience of the approach are shown as follows. First, the approach is a hitherto unexplored one to constructing CSS codes. Second, the judgment of a weakly self-dual code is entirely based on factor graphs. Namely, we consider a code a weakly self-dual one when the Tanner graph or convolutional factor graph of its dual code can be obtained by that of its own via our proposed transform T"R"-"L. Finally, we can obtain the generator matrix and parity-check matrix of a weakly self-dual code via factor graphs other than conventional algebra methods, which allow us avoid matrix computation to get them. An example is given to show how to construct quantum CSS code based on factor graphs. The method can be extended to other CSS codes.