LDPC Parity Check Matrix Generation for High Girth Codes

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Solution Overview

Problem

Conventional methods for generating parity check matrices for low-density parity-check (LDPC) codes result in matrices with low girth and uneven cycle distribution, reducing error correcting capability and requiring significant time for optimal positioning of circulant matrices.

Innovation Solution

A system and method that uses a processing circuitry to retrieve a base matrix representing valid and invalid positions for circulant matrices, determines values for valid positions based on a heuristic function, and replaces these positions with corresponding circulant matrices or null matrices to generate a parity check matrix with high girth and equal cycle distribution.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If circulant matrices are randomly selected and placed in the parity check matrix, then the generation process is simple, but the girth is low and cycle distribution is uneven

Engineering Contradiction:

Improveease of generating parity check matrixVSAvoiderror correcting capability

Core Design Contradiction:

Ease of manufactureVSReliability

Solution Approach 1:

The invention changes the parameters of circulant matrices by applying different shift operations to identity matrices to generate a set of circulant matrices with varying properties. By controlling the shift amounts and selecting specific circulant matrices from this set, the patent achieves both high girth and uniform cycle distribution while maintaining systematic generation process

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent pre-generates a set of circulant matrices by applying multiple shift operations to identity matrices before constructing the final parity check matrix. This preliminary action ensures that when circulant matrices are selected and placed in the parity check matrix, the desired properties of high girth and uniform cycle distribution are achieved without requiring random selection

Inventive Principle:

Principle #10Preliminary action

2Productivity

If circulant matrices are randomly selected and placed in the parity check matrix, then the generation process is fast, but significant time is required for optimal positioning

Engineering Contradiction:

Improvegeneration speed of parity check matrixVSAvoidtime for optimal positioning

Core Design Contradiction:

ProductivityVSLoss of time

Solution Approach 1:

The patent pre-generates a complete set of circulant matrices by applying multiple shift operations to identity matrices before the actual parity check matrix construction. This preliminary preparation ensures that during the subsequent assembly process, the optimal positioning is already determined by the systematic selection from the pre-generated set, eliminating the need for time-consuming optimization searches

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

By systematically varying the shift parameters when generating circulant matrices, the patent creates a structured set of matrices with known properties. This allows for direct selection and placement in the parity check matrix without requiring iterative optimization, thus maintaining fast generation speed while achieving optimal positioning

Inventive Principle:

Principle #35Parameter changes

3Ease of manufacture

If conventional methods are used to generate the parity check matrix, then the process is straightforward, but the girth is low and cycle distribution is uneven

Engineering Contradiction:

Improvesimplicity of generation methodVSAvoidgirth of parity check matrix

Core Design Contradiction:

Ease of manufactureVSLength of stationary object

Solution Approach 1:

The invention systematically changes the parameters of circulant matrices by applying different shift operations to identity matrices. By controlling the shift amounts and selecting specific circulant matrices from the generated set, the patent achieves high girth (increased length of the shortest cycle) while maintaining a straightforward, systematic generation process

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent applies different shift operations to different identity matrices to generate circulant matrices with locally optimized properties. Each circulant matrix in the set has specific characteristics determined by its shift operation, allowing the final parity check matrix to achieve high girth and uniform cycle distribution through strategic selection and placement

Inventive Principle:

Principle #3Local quality

Data Source

PatentUS11418216B2Method and system for generating parity check matrix for low-density parity check codes

Publication Date: 2022.08.16 SMART IOPS INC

AI summary

A system for generating a parity check matrix for low-density parity-check (LDPC) codes includes a memory and a processing circuitry that retrieves a base matrix from the memory. The base matrix represents sets of valid and invalid positions for a set of circulant matrices. The processing circuitry determines a value for each valid position based on a heuristic function. The value for each valid position indicates a corresponding circulant matrix of the set of circulant matrices. The processing circuitry replaces each valid position with the corresponding circulant matrix based on the determined value, and each invalid position with a null matrix, to generate the parity check matrix. The parity check matrix thus generated has a high girth and equal distribution of cycles within the parity check matrix.