Quasi-Cyclic LDPC Coding with Parameterized Inspection Matrices
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Solution Overview
Problem
Existing coding devices require significant storage space and time to switch between different low-density-parity-check (LDPC) codes due to the lack of regularity in the degrees of the inspection matrix, leading to inefficient error correction and increased storage needs.
Innovation Solution
A coding device that generates a quasi-cyclic LDPC code with a cyclic permutation matrix where the degrees of the inspection matrix are determined by a function λ(j−i), using a self-reciprocal polynomial with elements of the Galois field GF(q^2) as roots, and a mask pattern to reduce storage requirements and enable instant switching between different coding rates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the degrees of the inspection matrix are determined without regularity, then the error correction capability is maintained, but the storage space and switching time increase significantly
Solution Approach 1:
The patent applies parameter changes by introducing a regular structure to the degree values of the inspection matrix. Specifically, the degree at position (i, j) is determined by the formula degree = (a*i + b*j) mod (q-1), where a and b are constants. This regular parameterization transforms the storage requirement from storing all individual degree values to storing only the parameters a, b, and the mask pattern, significantly reducing storage space while maintaining error correction capability.
Solution Approach 2:
The patent uses copying by storing only the essential parameters (a, b, and mask pattern) that define the degree structure, rather than storing the complete inspection matrix. The actual degree values are generated on-demand by copying the computational pattern defined by the parameters, reducing storage requirements from O(r*q) to O(1) relative to the matrix size.
2Reliability
If the inspection matrix structure is complex without regularity, then the error correction performance is adequate, but the switching time between different LDPC codes increases
Solution Approach 1:
The patent enables fast switching by parameterizing the inspection matrix structure. When switching between different LDPC codes, only the parameters a, b, and the mask pattern need to be updated, rather than reloading the entire inspection matrix. This parameter-based approach reduces switching time from O(r*q) to O(1) operations, as the regular structure allows rapid regeneration of the matrix from parameters.
3Volume of stationary object
If regularity is introduced in the inspection matrix degrees, then storage space and switching time are reduced, but the flexibility in designing different LDPC codes may be limited
Solution Approach 1:
The patent achieves universality by designing a unified parameterized framework that can generate multiple different LDPC codes through varying the parameters a, b, and the mask pattern. The same regular structure formula degree = (a*i + b*j) mod (q-1) serves multiple functions by accommodating different code rates and lengths through parameter adjustment, maintaining design flexibility while preserving storage efficiency.
Solution Approach 2:
The patent maintains flexibility through parameter changes by allowing different values of a, b, and mask patterns to generate diverse LDPC codes with different properties. The regular structure is preserved, but the parameters can be adjusted to create codes with various rates, lengths, and error correction characteristics, ensuring adaptability across different application requirements.
Data Source
AI summary
A coding device includes: an inspection matrix generating module that generates a block inspection matrix; and a coding module that generates and outputs a code word from an input message by the inspection matrix. The inspection matrix generating module includes: a degree-allocation unit that prescribes function values of the block inspection matrix by the coefficients of a self-reciprocal polynomial expression; a weight distribution determination unit that prescribes the number of components that are non-zero matrices among the components of each block of the block inspection matrix using a mask pattern; a first degree-altering unit that considers the sum of the components of the k_r-th row block of the block inspection matrix as a cyclic permutation matrix; and a second degree-altering unit that prescribes the row-block number of components that are non-zero matrices among the components of each row block excluding said k_r-th row block of the clock inspection matrix.