Multi-Dimensional QC-LDPC Codes for Larger Codewords
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Solution Overview
Problem
Conventional one-dimensional quasi-cyclic (QC) low-density parity-check (LDPC) codes face limitations in increasing codeword size beyond 4 kilobytes, leading to inadequate performance due to a large number of short cycles and insufficient guaranteed minimum distance.
Innovation Solution
The implementation of multi-dimensional QC-LDPC codes, which involve determining dimensions using coprime numbers, generating distinct circulant rotation values based on root of unity and prime numbers, and assigning these values to circulant locations to encode data, thereby constructing more efficient codes with reduced short cycles and increased minimum distance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Length of stationary object
If conventional one-dimensional QC-LDPC codes are used with increasing codeword size, then the code length increases, but the number of short cycles increases and guaranteed minimum distance becomes insufficient
Solution Approach 1:
The patent transitions from conventional one-dimensional QC-LDPC codes to multi-dimensional QC-LDPC codes by introducing multiple dimensions (e.g., two-dimensional arrays of circulants). This dimensional expansion allows the code structure to achieve better minimum distance properties and reduced short cycles while maintaining scalability to larger codeword sizes, directly resolving the contradiction between code length and reliability.
2Length of stationary object
If conventional one-dimensional QC-LDPC codes are used with increasing codeword size, then the code length increases, but the number of short cycles increases
Solution Approach 1:
By organizing circulants in a multi-dimensional array structure rather than a one-dimensional sequence, the patent reduces the occurrence of short cycles in the Tanner graph. The multi-dimensional arrangement disperses the connections more effectively, preventing the formation of short cycles even as the code length increases, thus resolving the contradiction between code length and short cycle reduction.
Solution Approach 2:
The patent employs systematic parameter selection for constructing multi-dimensional QC-LDPC codes, including choosing appropriate dimensions, circulant sizes, and rotation values. By carefully selecting these parameters and using distinct circulant rotation values based on root of unity and prime numbers, the code structure achieves better cycle properties while maintaining the desired code length, resolving the contradiction between code length and short cycle reduction.
3Reliability
If multi-dimensional QC-LDPC codes are constructed with distinct circulant rotation values, then the guaranteed minimum distance increases, but the code complexity increases
Solution Approach 1:
The patent uses systematic parameter selection methods for constructing multi-dimensional QC-LDPC codes. By choosing appropriate dimensions, circulant sizes, and rotation values based on mathematical properties (root of unity, prime numbers), the construction process becomes more structured and manageable. This systematic approach achieves better minimum distance while controlling the complexity through regular patterns and mathematical constraints.
Solution Approach 2:
The patent divides the code construction into manageable segments by using multiple dimensions and blocking the parity-check matrix into circulant submatrices. Each circulant block can be independently constructed and rotated, allowing the overall complex code to be built from simpler components. This segmentation reduces the perceived complexity by breaking down the construction process into modular, reusable units.
Data Source
AI summary
The disclosure relates in some aspects to multi-dimensional quasi-cyclic (QC) low-density parity-check (LDPC) code generation. In one example, a controller of a data storage apparatus determines a plurality of dimensions for a code, the plurality of dimensions comprising a plurality of coprime numbers, generates distinct circulant rotation values based on at least a root of unity number and a prime number, assigns a different one of the distinct circulant rotation values to each of a plurality of circulant locations defined within the plurality of dimensions to generate the code, and encodes data using the code.