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.

A New Upper Bound on the Error Probability of Binary Linear Codes

2011 ◽  
Vol 403-408 ◽  
pp. 2852-2855
Author(s):  
Jun Guo ◽  
Li Yun Dai ◽  
Hong Wen Yang
Keyword(s):  
Performance Evaluation ◽  
Maximum Likelihood ◽  
Upper Bound ◽  
Error Probability ◽  
Linear Codes ◽  
Binary Linear Codes ◽  
Union Bound ◽  
Simulation Results ◽  
Error Probabilities

Performance evaluation of maximum-likelihood (ML) decoded binary linear codes is usually carried out using bounding techniques. In this paper, a new upper bound is presented to improve existing union bounds. The proposed upper bounding is based on probabilities of correct events, while the traditional union bound (UB) is on pair-wise error probabilities. Moreover, the improved upper bounding uses the intersection instead of the union of basic events. The theoretical and simulation results show that the proposed bound is tight than UB.

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.

scholarly journals Upper Bound on the Bit Error Probability of Systematic Binary Linear Codes via Their Weight Spectra

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jia Liu ◽  
Mingyu Zhang ◽  
Chaoyong Wang ◽  
Rongjun Chen ◽  
Xiaofeng An ◽  
...  
Keyword(s):  
Upper Bound ◽  
Error Probability ◽  
Linear Codes ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
High Signal ◽  
Binary Linear Codes ◽  
Enumerating Function ◽  
Bit Error Probability ◽  
Better Than

In this paper, upper bound on the probability of maximum a posteriori (MAP) decoding error for systematic binary linear codes over additive white Gaussian noise (AWGN) channels is proposed. The proposed bound on the bit error probability is derived with the framework of Gallager’s first bounding technique (GFBT), where the Gallager region is defined to be an irregular high-dimensional geometry by using a list decoding algorithm. The proposed bound on the bit error probability requires only the knowledge of weight spectra, which is helpful when the input-output weight enumerating function (IOWEF) is not available. Numerical results show that the proposed bound on the bit error probability matches well with the maximum-likelihood (ML) decoding simulation approach especially in the high signal-to-noise ratio (SNR) region, which is better than the recently proposed Ma bound.

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