Triple-Diagonal QC-LDPC Parity Matrix for Noisy Data Channels
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Solution Overview
Problem
Existing data transmission technologies face challenges in efficiently correcting errors over noisy media due to the complexity and cost of implementing low-density parity check (LDPC) codes, particularly with the double diagonal structure, which restricts the features of LDPC codes and increases implementation complexity.
Innovation Solution
A method and device for data transmission using a quasi-cyclic LDPC code with a parity matrix having a triple diagonal structure in the parity bit section, reducing the number of columns with a Hamming weight less than or equal to 2, thereby improving error correction capabilities without significantly increasing implementation complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a double diagonal structure is used in the parity matrix, then implementation complexity is reduced, but error correction capabilities are restricted
Solution Approach 1:
The parity matrix is segmented into multiple diagonal sections (first diagonal, second diagonal, and third diagonal) rather than using a single double diagonal structure. This segmentation allows each diagonal to contribute differently to error correction, improving overall reliability while maintaining manageable complexity through modular processing.
Solution Approach 2:
The invention adds a third diagonal dimension to the traditional double diagonal structure, transforming it from a two-diagonal configuration to a three-diagonal configuration. This dimensional expansion enables additional error correction pathways and improves the code's ability to correct errors without proportionally increasing implementation complexity.
2Reliability
If the number of columns with Hamming weight less than or equal to 2 is reduced, then error correction capabilities are improved, but implementation complexity increases
Solution Approach 1:
The invention changes the structural parameters of the parity matrix by introducing a third diagonal with specific patterns of non-zero elements. This parameter change reduces the number of columns with Hamming weight ≤2, thereby improving error correction capabilities. The third diagonal is carefully designed to distribute non-zero elements in a way that achieves this reduction without creating excessive complexity in the encoding and decoding processes.
Data Source
AI summary
A method includes defining a model matrix of size (n−k)×n, where n and k are positive integers, and where the model matrix includes a first sub-matrix corresponding to positions of data bits and a second sub-matrix corresponding to positions of parity bits. The second sub-matrix includes a multi-diagonal matrix with a triple diagonal structure. The triple diagonal structure includes a first and second central diagonals and a last row diagonal. Bits of the first and second central diagonal and the last row diagonal are equal to 1 and a remainder of bits in the multi-diagonal matrix are equal to 0. The method further includes: generating a compact matrix based on the model matrix; generating a parity matrix based on the compact matrix; determining the parity bits based on the parity matrix; and transmitting a codeword, based on the parity bits, over a channel and between communication devices.