Results 21 to 30 of about 8,529,401 (324)
Fault-tolerant gates via homological product codes [PDF]
Quantum, 2019 A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a given logical ...
Tomas Jochym-O'Connor
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About the generalized Hamming weights of matrix-product codes [PDF]
Computational and Applied MathematicsWe derive a general lower bound for the generalized Hamming weights of nested matrix-product codes, with a particular emphasis on the cases with two and three constituent codes.
Rodrigo San-José
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Cyclic product codes and their implementation
Information and Control, 1966 In many communication systems, variable-redundancy coding schemes are highly desirable either due to the fact that messages of various degrees of importance are present, or due to some change in the real communication channel. A class of “cyclic product codes” presented in this paper is capable of operating in variable redundancy modes. In the simplest
Donald T. Tang, Robert T. Chien
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Fast and Parallelizable Logical Computation with Homological Product Codes [PDF]
Physical Review XQuantum error correction is necessary to perform large-scale quantum computation but requires extremely large overheads in both space and time. High-rate quantum low-density-parity-check (qLDPC) codes promise a route to reduce qubit numbers, but ...
Qian Xu +6 more
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Iterative Bounded Distance Decoding of Product Codes with Scaled Reliability [PDF]
European Conference on Optical Communication, 2018 We propose a modified iterative bounded distance decoding of product codes. The proposed algorithm is based on exchanging hard messages iteratively and exploiting channel reliabilities to make hard decisions at each iteration. Performance improvements up
Alireza Sheikh, A. G. Amat, G. Liva
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2024 IEEE International Symposium on Information Theory (ISIT)6 pages, 1 figure, submitted to the IEEE ISIT ...
M. C. Coşkun
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Improved single-shot decoding of higher dimensional hypergraph product codes [PDF]
, 2022 In this work we study the single-shot performance of higher dimensional hypergraph product codes decoded using belief-propagation and ordered-statistics decoding [Panteleev and Kalachev, 2021].
O. Higgott, N. P. Breuckmann
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Sum-rank product codes and bounds on the minimum distance [PDF]
Finite Fields Their Appl., 2021 The tensor product of one code endowed with the Hamming metric and one endowed with the rank metric is analyzed. This gives a code which naturally inherits the sum-rank metric.
Gianira N. Alfarano +3 more
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ReShape: A Decoder for Hypergraph Product Codes [PDF]
IEEE Transactions on Information Theory, 2021 The design of decoding algorithms is a significant technological component in the development of fault-tolerant quantum computers. Often design of quantum decoders is inspired by classical decoding algorithms, but there are no general principles for ...
A. O. Quintavalle, E. Campbell
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Product construction of affine codes [PDF]
2014 IEEE International Symposium on Information Theory, 2014 Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of binary linear codes. Additionally, the constructions have the property that they are systematic.
Yeow Meng Chee +3 more
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