On a method of calculating the event error probability of convolutional codes with maximum likelihood decoding (Corresp.)

1979 ◽  
Vol 25 (6) ◽  
pp. 737-743 ◽  
Author(s):  
J. Schalkwijk ◽  
K. Post ◽  
J. Aarts
Keyword(s):  
Maximum Likelihood ◽  
Error Probability ◽  
Convolutional Codes ◽  
Maximum Likelihood Decoding

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.

2ℓ-Incorrigible set distributions of some linear codes by the finite geometry

2017 ◽  
Vol 09 (01) ◽  
pp. 1750012
Author(s):  
Lin-Zhi Shen ◽  
Fang-Wei Fu
Keyword(s):  
Maximum Likelihood ◽  
Linear Code ◽  
Error Probability ◽  
Linear Codes ◽  
Finite Geometry ◽  
Short Paper ◽  
List Decoding ◽  
Maximum Likelihood Decoding ◽  
Binary Linear Codes ◽  
Erasure Channels

The [Formula: see text]-incorrigible set distributions of binary linear codes over the erasure channels can be used to determine the decoding error probability of a linear code under maximum likelihood decoding and [Formula: see text]-list decoding. In this short paper, we give the [Formula: see text]-incorrigible set distributions of some linear codes by the finite geometry theory.

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