Non-Binary Parity Check Matrix Generation for Low-Storage QC-LDPC
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Solution Overview
Problem
Existing parity check matrices for QC-LDPC codes require large storage capacity and do not provide enhanced performance, as they need to store all element values, whereas the proposed solution generates non-binary parity check matrices based on intrinsic characteristics of binary matrices, reducing storage needs while enhancing performance.
Innovation Solution
A parity check matrix generator that converts binary cyclic permutation matrices into non-binary cyclic permutation matrices by applying weights and arithmetic operations, using a first memory for location information, a second memory for cyclic strength, and a third memory for determining matrix element sizes, thereby generating non-binary parity check matrices that require less storage and offer improved performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If binary parity check matrices are used for QC-LDPC codes, then all element values must be stored, but this results in large storage capacity requirements
Solution Approach 1:
The patent transforms the parity check matrix from binary form to non-binary form by applying weight values to cyclic permutation matrices. This parameter change allows the system to represent multiple binary matrices through a single non-binary matrix structure, reducing storage requirements while maintaining error correction capability.
Solution Approach 2:
The patent creates a compact representation (copy) of multiple binary parity check matrices by using non-binary cyclic permutation matrices with weight parameters. Instead of storing each binary matrix separately, a single parameterized structure generates all necessary matrices through parameter variation, significantly reducing storage capacity needs.
2Quantity of substance
If traditional binary parity check matrices are used, then storage requirements are high, but performance enhancement is not achieved
Solution Approach 1:
By introducing weight parameters and transforming to non-binary representation, the patent achieves both reduced storage capacity and enhanced error correction performance. The parameterized non-binary matrices provide more flexibility in representing code structures, leading to improved reliability while requiring less storage.
3Quantity of substance
If non-binary cyclic permutation matrices are generated from binary matrices, then storage capacity is reduced, but complex weight calculations are required
Solution Approach 1:
The patent pre-calculates and stores weight values in a weight table during system initialization. This preliminary action allows the complex weight calculations to be performed once beforehand, and the results are stored for quick reference during operation, reducing the computational burden during actual encoding and decoding processes.
Solution Approach 2:
The non-binary cyclic permutation matrices are designed to self-generate the required binary matrices through parameter expansion. The matrix structure inherently contains the information needed to reconstruct multiple binary matrices, making the system self-sufficient and reducing the need for external storage of multiple separate matrices.
Data Source
AI summary
A parity check matrix generator for generating a parity check matrix including non-binary cyclic permutation matrices may include: a first memory configured to store a first weight as location information on a non-binary cyclic permutation matrix within the parity check matrix; a second memory configured to store a second weight as cyclic strength of matrix elements of the non-binary cyclic permutation matrix; a third memory configured to store a third weight used to determine a size of a non-binary matrix element among the matrix elements of the non-binary cyclic permutation matrix; and a matrix generator configured to generate the non-binary cyclic permutation matrix by applying a non-binary value to matrix elements of 1's among matrix elements of a binary cyclic permutation matrix having a size corresponding to the non-binary cyclic permutation matrix and reflecting one or more of the first to third weights into the non-binary value.