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Trellis decoders are a general decoding technique first applied to qubit-based quantum error correction codes by Ollivier and Tillich in 2006.
The viterbi algorithm
G David Forney · 1973
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Optimal decoding of linear codes for minimizing symbol error rate (corresp.)
Lalit Bahl, John Cocke, Frederick Jelinek, and Josef Raviv · 1974
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On the inherent intractability of certain coding problems (corresp.)
Elwyn Berlekamp, Robert McEliece, and Henk Van Tilborg · 1978
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Efficient maximum likelihood decoding of linear block codes using a trellis
Jack Wolf · 1978
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Coset codes. ii. binary lattices and related codes
G David Forney · 1988
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Minimal trellises for block codes
Douglas J Muder · 1988
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The dynamics of group codes: state spaces, trellis diagrams, and canonical encoders
G David Forney and Mitchell D Trott · 1993
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Bounds on complexity of trellis decoding of linear block codes (in russian)
Victor Vasilievich Zyablov and Vladimir Removich Sidorenko · 1993
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On complexity of trellis structure of linear block codes
Tadao Kasami, Toyoo Takata, Toru Fujiwara, and Shu Lin · 1993
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Dimension/length profiles and trellis complexity of linear block codes
G David Forney · 1994
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The viterbi decoding complexity of linear block codes
Robert J McEliece · 1994
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On the trellis structure of block codes
Frank R Kschischang and Vladislav Sorokine · 1995
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Lower bounds on trellis complexity of block codes
Alec Lafourcade and Alexander Vardy · 1995
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Asymptotically good codes have infinite trellis complexity
A Lafourcade and Alexander Vardy · 1995
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On the trellis complexity of certain binary linear block codes
Øyvind Ytrehus · 1995
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On the bcjr trellis for linear block codes
Robert J McEliece · 1996
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Proof of a conjecture of mceliece regarding the expansion index of the minimal trellis
Alexander Vardy and Frank R Kschischang · 1996
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Trellis decoding complexity of linear block codes
Aaron B Kiely, Samuel J Dolinar, Robert J McEliece, Laura L Ekroot, and Wei Lin · 1996
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Minimal trellis design for linear codes based on the shannon product
Vladimir Sidorenko, Garik Markarian, and Bahram Honary · 1996
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A trellis-based recursive maximum-likelihood decoding algorithm for binary linear block codes
Toru Fujiwara, Hiroshi Yamamoto, Tadao Kasami, and Shu Lin · 1998
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Nonbinary quantum codes
Eric M Rains · 1999
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Constructions of generalized concatenated codes and their trellis-based decoding complexity
Robert Morelos-Zaragoza, Toru Fujiwara, Tadao Kasami, and Shu Lin · 1999
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Exact performance of concatenated quantum codes
Benjamin Rahn, Andrew C. Doherty, and Hideo Mabuchi · 2002
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Confinement-higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
Chenyang Wang, Jim Harrington, and John Preskill · 2003
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Sparse-graph codes for quantum error correction
David JC MacKay, Graeme Mitchison, and Paul L McFadden · 2004
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Simplified trellis decoding of block codes by selective pruning
Eric Bertrand and Fabrice Labeau · 2004
Earlier work this paper cites.
Trellises for stabilizer codes: definition and uses
Harold Ollivier and Jean-Pierre Tillich · 2006
Earlier work this paper cites.
Nonbinary stabilizer codes over finite fields
Avanti Ketkar, Andreas Klappenecker, Santosh Kumar, and Pradeep Kiran Sarvepalli · 2006
Cited alongside, same era.
Optimal and efficient decoding of concatenated quantum block codes
David Poulin · 2006
Cited alongside, same era.
Bounds on the minimum distance of linear codes and quantum codes
Markus Grassl · 2007
Cited alongside, same era.
On the iterative decoding of sparse quantum codes
David Poulin and Yeojin Chung · 2008
Cited alongside, same era.
Standard forms of stabilizer and normalizer matrices for additive quantum codes
Ruihu Li, Zongben Xu, and Xueliang Li · 2008
Cited alongside, same era.
Handbook of mamga functions: Volume 13 - coding theory and cryptography
John Cannon, Wieb Bosma, Claus Fieker, and Allan Steel · 2008
A simple decoder for topological codes
James Wootton · 2015
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Cellular-automaton decoders for topological quantum memories
Michael Herold, Earl T Campbell, Jens Eisert, and Michael J Kastoryano · 2015
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Fast fault-tolerant decoder for qubit and qudit surface codes
Fern HE Watson, Hussain Anwar, and Dan E Browne · 2015
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Improved hdrg decoders for qudit and non-abelian quantum error correction
Adrian Hutter, Daniel Loss, and James R Wootton · 2015
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Almost-linear time decoding algorithm for topological codes
Nicolas Delfosse and Naomi H Nickerson · 2017
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Cellular automaton decoders of topological quantum memories in the fault tolerant setting
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Cited alongside, same era.
Graphical algorithms and threshold error rates for the 2d colour code
David S Wang, Austin G Fowler, Charles D Hill, and Lloyd Christopher L Hollenberg · 2009
Cited alongside, same era.
Quantum serial turbo codes
David Poulin, Jean-Pierre Tillich, and Harold Ollivier · 2009
Cited alongside, same era.
Logical operators of quantum codes
Mark M Wilde · 2009
Cited alongside, same era.
Error threshold for color codes and random three-body ising models
Helmut G Katzgraber, H Bombin, and MA Martin-Delgado · 2009
Cited alongside, same era.
Fast decoders for topological quantum codes
Guillaume Duclos-Cianci and David Poulin · 2010
Cited alongside, same era.
A renormalization group decoding algorithm for topological quantum codes
Guillaume Duclos-Cianci and David Poulin · 2010
Cited alongside, same era.
Michael Herold, Michael J Kastoryano, Earl T Campbell, and Jens Eisert · 2017
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Tensor-network simulations of the surface code under realistic noise
Andrew S Darmawan and David Poulin · 2017
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Neural decoder for topological codes
Giacomo Torlai and Roger G Melko · 2017
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Comparison of memory thresholds for planar qudit geometries
Jacob Marks, Tomas Jochym-O’Connor, and Vlad Gheorghiu · 2017
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On the local equivalence of 2d color codes and surface codes with applications
Arun B Aloshious, Arjun Nitin Bhagoji, and Pradeep Kiran Sarvepalli · 2018
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Linear-time general decoding algorithm for the surface code
Andrew S Darmawan and David Poulin · 2018
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Ultrahigh error threshold for surface codes with biased noise
David K Tuckett, Stephen D Bartlett, and Steven T Flammia · 2018
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Machine-learning-assisted correction of correlated qubit errors in a topological code
Paul Baireuther, Thomas E O’Brien, Brian Tarasinski, and Carlo WJ Beenakker · 2018
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Deep neural decoders for near term fault-tolerant experiments
Christopher Chamberland and Pooya Ronagh · 2018
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Efficient color code decoders in d ≥ 2 d\geq 2 dimensions from toric code decoders
Aleksander Kubica and Nicolas Delfosse · 2019
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Cellular-automaton decoders with provable thresholds for topological codes
Aleksander Kubica and John Preskill · 2019
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Neural network decoder for topological color codes with circuit level noise
Paul Baireuther, Marcello D Caio, Ben Criger, Carlo WJ Beenakker, and Thomas E O’Brien · 2019
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Neural decoder for topological codes using pseudo-inverse of parity check matrix
Chaitanya Chinni, Abhishek Kulkami, Dheeraj MPai, Kaushik Mitra, and Pradeep K Sarvepalli · 2019
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Advantages of versatile neural-network decoding for topological codes
Nishad Maskara, Aleksander Kubica, and Tomas Jochym-O’Connor · 2019
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Degenerate quantum ldpc codes with good finite length performance
Pavel Panteleev and Gleb Kalachev · 2019
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Local equivalence of qudit color codes and toric codes
Arun B Aloshious and Pradeep Kiran Sarvepalli · 2019
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Fault-tolerant weighted union-find decoding on the toric code
Shilin Huang, Michael Newman, and Kenneth R Brown · 2020
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Decoding across the quantum ldpc code landscape
Joschka Roffe, David R White, Simon Burton, and Earl T Campbell · 2020
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Triangular color codes on trivalent graphs with flag qubits
Christopher Chamberland, Aleksander Kubica, Theodore J Yoder, and Guanyu Zhu · 2020
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Union-find decoders for homological product codes
Nicolas Delfosse and Matthew B Hastings · 2021
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Toward a union-find decoder for quantum ldpc codes
Nicolas Delfosse, Vivien Londe, and Michael Beverland · 2021
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General tensor network decoding of 2d pauli codes
Christopher Thomas Chubb · 2021
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