Towards Practical Near-Maximum-Likelihood Decoding of Error-Correcting Codes: An Overview

2021 ◽  
Author(s):  
Thibaud Tonnellier ◽  
Marzieh Hashemipour ◽  
Nghia Doan ◽  
Warren J. Gross ◽  
Alexios Balatsoukas-Stimming
Keyword(s):  
Maximum Likelihood ◽  
Error Correcting Codes ◽  
Maximum Likelihood Decoding

Maximum likelihood decoding of RLL-FEC array codes on partial response channels

1993 ◽  
Vol 29 (16) ◽  
pp. 1406 ◽  
Author(s):  
G.S. Markarian ◽  
M. Naderi ◽  
B. Honary ◽  
A. Popplewell ◽  
J.J. O'Reilly
Keyword(s):  
Maximum Likelihood ◽  
Partial Response ◽  
Maximum Likelihood Decoding ◽  
Partial Response Channels ◽  
Array 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.

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