Non-Binary LDPC Parity Matrix Layout for Lower-Complexity Coding
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Solution Overview
Problem
There is a lack of specific solutions for generating parity check matrices and encoding/decoding non-binary Low Density Parity Check (LDPC) codes, as well as transmitting/receiving signals using non-binary LDPC codes in conventional communication systems.
Innovation Solution
The proposed solution involves an apparatus and method for generating and using parity check matrices in non-binary LDPC codes, where the matrices are divided into blocks corresponding to information and parity parts, with non-binary essential matrices arranged in a lower triangular form and multiplexed using elements from Galois Field (GF)(q=2p) and permutation matrices, facilitating efficient encoding and decoding in communication systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If non-binary LDPC codes are used to enhance data transmission reliability, then error correction performance is improved, but encoding and decoding complexity increases due to lack of specific solutions for parity check matrix generation and signal processing
Solution Approach 1:
The parity check matrix is segmented into information blocks and parity blocks, with each block containing specific patterns of non-zero elements. This segmentation allows the encoder to process only the information blocks to generate parity blocks, significantly reducing encoding complexity while maintaining the error correction capabilities of non-binary LDPC codes
Solution Approach 2:
The patent pre-defines the structure and properties of the parity check matrix, including the arrangement of non-zero elements and their relationships between blocks. This preliminary design enables the encoder to directly compute parity blocks from information blocks without complex iterative processes, reducing real-time encoding complexity
2Ease of manufacture
If conventional LDPC encoding schemes are applied to non-binary codes, then implementation is straightforward, but encoding complexity increases and performance is suboptimal due to parity nodes with degree 1
Solution Approach 1:
The patent applies different structural properties to different blocks of the parity check matrix. Information blocks contain non-zero elements arranged in specific patterns, while parity blocks have complementary patterns. This local differentiation ensures that no parity nodes have degree 1, optimizing decoding performance while maintaining implementation feasibility through structured design
3Productivity
If non-binary essential matrices are multiplexed with permutation matrices, then encoding complexity is minimized and decoding performance is enhanced, but matrix generation and arrangement complexity increases
Solution Approach 1:
The patent pre-establishes the multiplexing structure between non-binary essential matrices and permutation matrices in the parity check matrix design. The positions and patterns of non-zero elements are predetermined, allowing efficient encoding operations while the matrix generation complexity is managed through systematic design rules rather than arbitrary construction
Data Source
AI summary
An apparatus and method for encoding/decoding a non-binary low density parity check (LDPC) code in a communication system. The apparatus and method includes receiving an information vector; generating a non-binary LDPC code by encoding the information vector into a non-binary LDPC code according to a non-binary LDPC encoding scheme.