LDPC Matrix Scaling for Larger Block Codes With Lower Hardware Complexity
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Solution Overview
Problem
Existing methods for increasing the block length of low-density parity-check (LDPC) codes are limited, leading to increased hardware complexity and compatibility issues with existing systems, making it difficult to enhance error correction capabilities and system performance efficiently.
Innovation Solution
A scaling method for LDPC codes that involves obtaining an original matrix, forming permutation matrices through random shifts, replacing component codes with these matrices, adjusting code length and rate, and outputting a global coupled matrix, allowing for the construction of larger block codes from shorter ones while maintaining compatibility with existing systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the block code length is increased to improve error correction capability, then the error correction capability is improved, but the hardware complexity of encoders and decoders increases
Solution Approach 1:
The patent segments a large block LDPC code into multiple smaller component codes (e.g., 512-bit component codes). Each component code can be encoded and decoded independently using identical hardware modules. The large block code is constructed by parallel concatenation of these component codes with specific coupling constraints, allowing error correction capability of large blocks while using replicated smaller hardware units rather than a single complex large-block processor.
Solution Approach 2:
The patent implements a hierarchical nested structure where small component codes (e.g., 512 bits) are nested within larger block codes (e.g., 4K bits). Each level of nesting uses the same structural patterns and coupling constraints. This nested architecture allows systematic scaling from small to large block lengths while reusing the same base hardware design, reducing overall complexity through pattern repetition rather than unique large-scale design.
2Length of moving object
If a new mother code is designed to increase block code length, then the block code length is increased, but the system development time increases and compatibility with previous systems is lost
Solution Approach 1:
The patent creates a universal LDPC code construction framework where a single base matrix structure and coupling constraint set can generate multiple different LDPC codes with various block lengths (e.g., 2K, 4K, 8K bits) by simply changing the number of component codes concatenated and their arrangement patterns. This universal framework eliminates the need to design separate mother codes for each block length, significantly reducing development time while maintaining compatibility through consistent structural patterns.
Solution Approach 2:
The patent enables systematic parameter scaling where block length is controlled by changing the number of component codes (M) and their arrangement in the global coupled matrix, rather than redesigning the entire code structure. By varying parameters such as component code length, number of components, and coupling density while maintaining the same fundamental construction rules, codes of different lengths can be generated from a single base design, reducing development time and ensuring compatibility.
3Length of moving object
If conventional methods (shortening, puncturing, extension) are used to adjust code length, then the code length can be adjusted, but the block code length cannot be increased
Solution Approach 1:
The patent transitions from one-dimensional code length adjustment (shortening/puncturing existing codes) to two-dimensional scaling by varying both the number of component codes (M) and their individual lengths. The global coupled matrix structure provides an additional dimension where component codes can be arranged in different configurations (parallel, serial, nested) to achieve various effective block lengths. This multi-dimensional approach enables genuine code length expansion beyond the limitations of conventional single-code manipulation methods.
Data Source
AI summary
A low-density parity-check code scaling method is disclosed. The method includes following steps: obtaining the original low-density parity-check matrix; forming the permutation matrices with the random row shift or the random column shift to the identity matrix; replacing the component codes by the permutation matrices and the all-zero matrix to form the extended low-density parity-check matrix; adjusting the code length and the code rate to form the global coupled low-density parity-check matrix; and outputting the global coupled low-density parity-check code.