Thresholds of precoded (3,6) LDPC codes under iterative and maximum-likelihood decodings

2012 ◽  
Author(s):  
Huijuan Zheng ◽  
Sheng Tong
Keyword(s):  
Maximum Likelihood ◽  
Ldpc Codes

scholarly journals On maximum-likelihood decoding with circuit-level errors

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 304
Author(s):  
Leonid P. Pryadko
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Error Probability ◽  
Ldpc Codes ◽  
Quantum Codes ◽  
Quantum Code ◽  
Maximum Likelihood Decoding ◽  
Measurement Circuit ◽  
Equivalence Group ◽  
Error Probability Distribution

Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and Shi. This gives a prescription for maximum-likelihood decoding with a given measurement circuit. Marginal distributions for subsets of circuit errors are also analyzed; these generate a family of related asymmetric LDPC codes of varying degeneracy. More generally, such a family is associated with any quantum code. Implications for decoding highly-degenerate quantum codes are discussed.

Maximum Likelihood Erasure Decoding of LDPC Codes: Pivoting Algorithms and Code Design

2012 ◽  
Vol 60 (11) ◽  
pp. 3209-3220 ◽  
Author(s):  
Enrico Paolini ◽  
Gianluigi Liva ◽  
Balazs Matuz ◽  
Marco Chiani
Keyword(s):  
Maximum Likelihood ◽  
Ldpc Codes ◽  
Code Design
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