Probability Density Function Approximation Using Piecewise Linear Mapping
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing storage and communication systems face challenges in computing probability values for received values with arbitrary probability density functions, which are more complex than those with Gaussian distributions, due to distortions like back pattern dependency and intercell interference in flash memory devices.
Innovation Solution
The method approximates a target probability density function for received values by minimizing the squared error between the target distribution and a predefined distribution, such as a Gaussian distribution, using a piecewise linear mapping function with segment-specific parameters, allowing for adaptive updates based on measured distributions and performance factors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a predefined distribution (e.g., Gaussian) is used to compute probability values, then computational complexity is reduced, but accuracy deteriorates when the actual distribution is arbitrary due to distortions
Solution Approach 1:
The patent transforms the arbitrary distribution into a parameterized form by fitting a family of distributions (e.g., Gaussian with varying mean and variance) to the observed data. This allows the system to adapt the distribution parameters to match the actual characteristics of the received values, thereby maintaining accuracy while using computationally simple predefined distribution forms.
Solution Approach 2:
The system dynamically estimates distribution parameters from the actual received values rather than using fixed predefined parameters. By continuously adapting the mean, variance, or other distribution parameters to match the observed data characteristics, the system achieves both computational efficiency and high accuracy in probability value computation.
2Measurement precision
If the actual arbitrary distribution is used to compute probability values, then accuracy is maintained, but computational complexity increases significantly
Solution Approach 1:
The patent creates a simplified copy or approximation of the complex arbitrary distribution using predefined distribution forms. By copying the essential statistical characteristics (mean, variance, skewness, etc.) into a parameterized distribution model, the system retains the accuracy of the original distribution while using much simpler computational methods for probability value calculation.
Solution Approach 2:
The system segments the complex distribution problem into manageable parts by dividing the parameter space into discrete categories or using piecewise approximations. This segmentation allows the system to handle the arbitrary distribution through a series of simpler, predefined distribution segments, reducing overall computational complexity while maintaining accuracy.
3Measurement precision
If distribution parameters are estimated from measured data, then accuracy improves, but processing time increases due to parameter estimation requirements
Solution Approach 1:
The patent performs distribution parameter estimation in advance during system initialization or calibration phases, rather than computing parameters in real-time during data processing. By pre-characterizing the distribution parameters from training data or initial measurements, the system eliminates the time-consuming parameter estimation step during actual operation, achieving both high accuracy and fast processing.
Solution Approach 2:
The system uses self-service techniques where the distribution parameters are automatically estimated from the data itself without requiring external intervention or complex manual calibration. By implementing automated parameter estimation algorithms that leverage the data's own statistical properties, the system reduces processing time while maintaining high accuracy in probability value computation.
Data Source
AI summary
Methods and apparatus are provided for approximating a probability density function or distribution for a received value in communication or storage systems. A target distribution is approximated for a received value in one or more of a communication system and a memory device, by substantially minimizing a squared error between the target distribution of the received values and a second distribution obtained by mapping a predefined distribution, such as a Gaussian distribution, through a mapping function, wherein the second distribution has an associated set of parameters. The mapping function can be, for example, a piecewise linear function. The second distribution has a plurality of segments and each of the segments has an associated set of parameters. The associated set of parameters can be used to compute probability values, soft data values or log likelihood ratios.