QC-LDPC Parity Check Matrix Offsets for Adaptive Code Lengths
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Solution Overview
Problem
Existing Low-Density-Parity-Check (LDPC) coding systems, particularly quasi-cyclic (QC) LDPC codes, require significant hardware resources for encoding and decoding due to the complexity of parity check matrices and algorithms, which limits efficiency and increases resource consumption.
Innovation Solution
The implementation of a method that uses lifting functions and circulant size offsets to generate child codes from mother codes, allowing for efficient encoding and decoding with reduced hardware requirements by determining optimal circulant sizes and lifting functions based on information length, code rate, and decoder specifications, and storing these in a lifting table for adaptive use.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If QC LDPC codes with traditional parity check matrices are used, then error correction capability is maintained, but hardware resources and complexity increase significantly
Solution Approach 1:
The parity check matrix is segmented into multiple sub-matrices, each handling specific portions of the codeword. This segmentation allows parallel processing during encoding and decoding operations, reducing the computational burden on single hardware components while maintaining the overall error correction capability of the QC LDPC code.
Solution Approach 2:
The patent implements a nested structure where child codes are derived from mother codes through systematic lifting operations. The child code's parity check matrix is constructed by lifting the mother code's matrix with specific circulant permutations, creating a hierarchical relationship that reduces hardware resources while preserving error correction properties.
2Reliability
If traditional LDPC encoding methods are used, then code reliability is maintained, but encoding and decoding efficiency decreases
Solution Approach 1:
The patent pre-computes and stores lifting tables containing optimal circulant permutation values and sub-matrix configurations for various code rates and block lengths. During actual encoding and decoding operations, these pre-computed values are directly applied, eliminating the need for complex real-time calculations and significantly improving processing efficiency while maintaining code reliability.
Solution Approach 2:
The patent systematically varies key parameters including circulant size, lifting degree, and sub-matrix dimensions to optimize the balance between error correction performance and processing speed. By adjusting these parameters based on specific application requirements, the system achieves both high reliability and improved encoding/decoding efficiency.
3Ease of manufacture
If fixed parity check matrices are used, then implementation is simplified, but adaptability to different code rates and lengths is reduced
Solution Approach 1:
The patent implements dynamic configurability through lifting tables that allow the system to adapt the parity check matrix structure based on the desired code rate and block length. The lifting degree and circulant permutation values can be dynamically adjusted by selecting different entries from the lifting tables, enabling the same hardware implementation to support multiple code configurations without sacrificing implementation simplicity.
Data Source
AI summary
A method and system for offset lifting is provided. In an embodiment, a method for encoding data includes receiving a K-bit source word input. The method also includes encoding the K-bit source word input according to a LDPC code, a lifting function, and a circulant size offset to generate an N-bit code word output. The circulant size and lifting function are determined according to an information length, a code rate, and a decoder. The method also includes storing the N-bit code word output in input/output memory.