LDPC Parity Check Matrix Permutation for Lower-Complexity Encoding
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Solution Overview
Problem
The complexity of LDPC encoding and decoding processes increases with the size of the parity check matrix, making it resource-intensive and challenging to support retransmission functions like ARQ or HARQ effectively.
Innovation Solution
The method involves generating a parity check matrix by applying row and column permutation patterns to a base matrix, replacing indices with corresponding sub-matrices, and permuting the encoded bit stream according to the inverse column permutation pattern to reduce complexity and enhance efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the size of the parity check matrix is increased to improve error correction capability, then the reliability of data transmission is improved, but the complexity of encoding and decoding processes increases
Solution Approach 1:
The parity check matrix is divided into multiple sub-matrices arranged in a block structure. Each sub-matrix corresponds to a specific section of the code, allowing the encoding and decoding processes to be performed on smaller, more manageable blocks rather than the entire large matrix at once. This segmentation reduces the computational complexity while maintaining the overall error correction capability through the coordinated operation of sub-matrices.
Solution Approach 2:
The patent introduces a two-dimensional block structure to the parity check matrix, where sub-matrices are arranged in rows and columns. This dimensional organization allows for structured processing patterns that reduce complexity, such as processing entire blocks simultaneously or using the block structure to optimize memory access patterns during encoding and decoding operations.
2Productivity
If the parity check matrix size is increased to support more data bits, then the productivity of data transmission is improved, but the resource requirements increase
Solution Approach 1:
By segmenting the large parity check matrix into smaller sub-matrices, the patent enables more efficient utilization of computational resources. Each sub-matrix can be processed independently or in parallel, reducing the peak memory requirements and allowing the system to handle larger data volumes without linearly increasing resource consumption.
Solution Approach 2:
The patent changes the structural parameters of the parity check matrix by introducing a block pattern with specific arrangements of sub-matrices. This parameter change allows the system to achieve higher data transmission capacity while controlling resource requirements through the regular, repeating structure of the blocks, which can be generated algorithmically rather than stored entirely.
3Ease of operation
If a structured parity check matrix with permutation patterns is used to reduce complexity, then the ease of operation is improved, but the device complexity increases due to additional permutation steps
Solution Approach 1:
The permutation patterns are predetermined and stored as lookup tables or generation rules. During encoding and decoding operations, the system applies these pre-defined patterns without performing complex real-time calculations. This preliminary preparation of permutation patterns simplifies the actual encoding/decoding operations while the complexity is shifted to the initial setup phase.
Solution Approach 2:
The patent uses repeating block patterns where identical or similar sub-matrices are copied and arranged in specific positions within the larger parity check matrix. This copying approach reduces the amount of unique data that needs to be stored and processed, as the same sub-matrix structures can be reused multiple times throughout the matrix, simplifying the overall operation despite the larger matrix size.
Data Source
AI summary
A method for encoding data using a parity check matrix is disclosed. The method for encoding data using a parity check matrix comprises generating a fourth base matrix by applying a row permutation pattern and a column permutation pattern to rows and columns of a third base matrix, respectively, the third base matrix including a plurality of indexes, each of the plurality of indexes indicating a sub-matrix; generating the parity check matrix by replacing each index of the fourth base matrix with a corresponding sub-matrix; outputting an encoded bit stream by encoding an input bit stream using the generated parity check matrix; and permuting an order of sequences of the encoded bit stream according to an inverse of the column permutation pattern.