LDPC Code Lifting for Rate-Adaptive QC Parity-Check Matrices
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Solution Overview
Problem
Existing Low-Density-Parity-Check (LDPC) coding systems, particularly quasi-cyclic (QC) LDPC, require significant hardware resources for encoding and decoding due to the storage and use of parity check matrices, which limits efficiency and flexibility in supporting varying information lengths and coding rates.
Innovation Solution
The method involves lifting procedures to derive child parity check matrices (PCMs) from base PCMs using circulant sizes, lifting functions, and shifts, allowing for adaptive coding rates and lengths, reducing resource consumption by using a limited set of coding schemes that can switch between different lift values and PCMs based on changing conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If quasi-cyclic LDPC codes with QC parity-check matrices are used to support varying information lengths and coding rates, then adaptability is improved, but hardware resource consumption increases due to storage and processing of multiple PCMs
Solution Approach 1:
The patent applies universality by using a single base PCM that can serve multiple functions through the lifting operation. Instead of storing separate PCMs for different code rates and lengths, one base PCM is lifted with different parameters (lift size, offset values) to generate child PCMs on-demand, making the system universal across multiple coding scenarios.
Solution Approach 2:
The patent changes parameters of the base PCM through the lifting operation. By varying the lift size Z and offset values while keeping the base PCM structure constant, the system generates different child PCMs with adapted properties for different information lengths and coding rates, rather than changing the entire PCM matrix.
2Adaptability or versatility
If multiple base PCMs are stored to support different coding schemes, then adaptability is improved, but storage space consumption increases
Solution Approach 1:
The patent uses copying by generating child PCMs as copies of the base PCM through the lifting operation. Instead of storing multiple original PCMs, the system creates derived copies on-demand by applying lifting transformations to the single base PCM, significantly reducing storage requirements while maintaining support for multiple coding schemes.
3Adaptability or versatility
If lifting procedures with multiple combinations of circulant sizes, lifting functions, and shifts are used, then coding flexibility is improved, but computational complexity increases
Solution Approach 1:
The patent applies dynamics by making the lifting parameters (lift size, offset values) adjustable and changeable during operation. The system can dynamically select different lifting configurations based on the required code rate and information length, allowing flexible adaptation without requiring multiple static PCM structures.
Data Source
AI summary
A method for generating a code, a method for encoding and decoding data, and an encoder and a decoder performing the encoding and decoding are disclosed. In an embodiment, a method for lifting a child code from a base code for encoding and decoding data includes determining a single combination of a circulant size, a lifting function, and a labelled base matrix PCM according to an information length and a code rate using data stored in a lifting table. The lifting table was defined at a code generation stage. The method also includes calculating a plurality of shifts for the child code. Each shift is calculated by applying the lifting function to the labelled base matrix PCM with a defined index using the circulant size and using the derived child PCM to encode or decode data.