Circulant LDPC Parity Check Matrix for Lower Decoding Errors
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Solution Overview
Problem
Existing LDPC parity check matrices, such as those used in MoCA networks, have a lower triangular structure that leads to increased decoding errors and iterations due to reduced connections with the codeword, particularly in the last parity column with a column weight of one.
Innovation Solution
A robust LDPC parity check matrix is designed with a systematic and parity portion, where the column weights of the parity portion are uniform, achieved through cyclic shifts of identity submatrices, allowing for simultaneous LLR calculations across check nodes without common variable nodes, thereby reducing decoding errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a lower triangular structure is used for the LDPC parity check matrix, then the matrix structure is simplified and easier to implement, but decoding errors increase and decoding iterations increase due to reduced connections with the codeword
Solution Approach 1:
The patent applies asymmetry by transforming the lower triangular structure into a circulant structure where the parity check matrix H2 is composed of circulant submatrices with uniform column weights. This asymmetric transformation from triangular to circulant form maintains structural simplicity while improving decoding reliability through enhanced connectivity patterns in the Tanner graph representation.
Solution Approach 2:
The patent changes the structural parameters of the parity check matrix by enforcing uniform column weights across all columns of H2. This parameter change from variable column weights in lower triangular form to uniform column weights in circulant form resolves the contradiction by maintaining implementation simplicity while significantly improving decoding performance and reducing iteration counts.
2Ease of manufacture
If the last parity column has a column weight of one in the lower triangular structure, then the matrix construction is simplified, but decoding errors significantly increase due to reduced connections
Solution Approach 1:
The patent applies homogeneity by ensuring all columns in the parity portion H2 have the same column weight. This eliminates the heterogeneous column weight distribution where the last column had weight one, creating uniform connectivity across all parity bits and significantly improving decoding accuracy while maintaining construction simplicity through the circulant structure.
3Measurement precision
If variable nodes are recalculated and updated during iterative LLR calculation, then decoding accuracy is improved, but simultaneous calculation across check nodes is restricted due to shared variable nodes
Solution Approach 1:
The patent applies segmentation by organizing the parity check matrix into distinct circulant submatrices that can be processed in parallel layers. The segmentation of H2 into circulant blocks with uniform column weights allows the decoder to divide variable nodes into separate groups that can be updated simultaneously across different check nodes, improving parallel processing capability while maintaining iterative decoding accuracy.
Data Source
AI summary
An LDPC parity check matrix, includes a systematic portion having a plurality of systematic elements having a value, the value each systematic element determining a cyclic shift to be applied to rows of an identity submatrix corresponding to that element; and a parity portion having a plurality of panty elements having a value, the value of each parity element determining a cyclic shift to be applied to rows of an identity submatrix corresponding to that element; wherein the weights of each column of a group of columns of the parity portion is the same. The LDPC parity check matrix may be used for data access, communication and storage, and may be used, for example for communications among a plurality of network nodes.