LDPC Parity Check Matrix Layout for Lower Encoding Complexity
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Solution Overview
Problem
The high complexity and memory requirements of encoding and decoding data using large parity check matrices in wireless communication systems, particularly with Low Density Parity Check (LDPC) codes, pose challenges in efficient data transmission and reception.
Innovation Solution
The method involves generating a parity matrix using a base matrix expanded by permutation and zero matrices, allowing for efficient encoding and decoding by minimizing the reliance on complex generator matrices and optimizing memory usage through permutation information and matrix shifting techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a large parity check matrix is used for LDPC encoding and decoding, then error correction capability is improved, but device complexity and memory requirements increase
Solution Approach 1:
The large parity check matrix is divided into multiple sub-matrices, where each sub-matrix corresponds to a specific portion of the codeword. The encoding process processes data in segments corresponding to these sub-matrices rather than handling the entire large matrix at once, reducing computational complexity while maintaining the error correction capability provided by the complete matrix structure.
Solution Approach 2:
The patent transforms the traditional two-dimensional parity check matrix into a three-dimensional structure by adding a time dimension through progressive transmission. The parity check matrix is divided into multiple sub-matrices transmitted in sequence, allowing the receiver to gradually accumulate and process information, thereby reducing the memory burden and computational complexity at any given moment while preserving the overall error correction capability.
2Reliability
If a large parity check matrix is used for LDPC encoding and decoding, then error correction capability is improved, but memory requirements increase
Solution Approach 1:
The parity check matrix is segmented into multiple sub-matrices that can be stored and processed in smaller units. Instead of requiring the entire large matrix to be held in memory simultaneously, the system stores only the current sub-matrix being processed along with accumulated syndrome information, significantly reducing the memory space required while maintaining the full error correction capability through progressive processing.
Solution Approach 2:
By introducing the time dimension through progressive transmission of sub-matrices, the patent converts a memory-intensive spatial problem into a time-based processing problem. The receiver processes sub-matrices sequentially over time, accumulating syndrome information gradually, which reduces the peak memory requirements compared to holding the entire large parity check matrix in memory at once.
3Ease of manufacture
If complex generator matrices are used for encoding, then encoding capability is improved, but device complexity increases
Solution Approach 1:
The patent extracts and utilizes only the essential parity check matrix structure for encoding operations, eliminating the need for complex generator matrices. By focusing on the parity check relationships defined by H×G=0 and using the parity check matrix directly for syndrome calculation and encoding guidance, the system achieves effective encoding capability with simpler mathematical operations and reduced computational complexity.
Data Source
AI summary
A method of encoding data using low density parity check (LDPC) code defined by a m×n parity check matrix is disclosed. More specifically, the method includes encoding input source data using the parity check matrix, wherein the parity check matrix comprises a plurality of z×z sub-matrices of which row weights and column weights are ‘0’ or ‘1’.