LDPC Lifting With Labeled Base Matrices for Adaptive Code Rates
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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, and struggle with efficient adaptation to varying information lengths and coding rates, leading to resource-intensive storage and processing needs.
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 encoding and decoding by switching between different labeled PCMs based on changing coding rates and information lengths, thereby optimizing resource usage and performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If QC LDPC encoding and decoding algorithms are used, then data recovery capability is improved, but hardware resource consumption increases
Solution Approach 1:
The patent segments the LDPC code into a base code and multiple child codes derived through lifting operations. The base code is stored in a lookup table, while child codes are generated on-demand by applying lifting functions with different parameters (circulant sizes, shift values). This segmentation allows the system to maintain a compact base representation while generating diverse codes as needed, reducing overall hardware resource requirements.
Solution Approach 2:
The patent employs parameter changes by varying lifting parameters (circulant size Z, shift values s[i,j], lifting functions f_i) to generate different child codes from a single base code. This allows the system to adapt to different coding rates and information lengths without storing multiple complete code definitions, thereby reducing hardware resource consumption while maintaining data recovery capability.
2Adaptability or versatility
If multiple base PCMs are stored for different coding rates, then adaptability to varying coding rates is improved, but storage requirements increase
Solution Approach 1:
The patent makes a single base PCM universal by enabling it to generate multiple child codes suitable for different coding rates and information lengths through lifting operations. The base code stored in the lookup table serves as a universal template that can be transformed into various child codes by adjusting lifting parameters, eliminating the need to store separate base PCMs for each coding rate.
Solution Approach 2:
The patent performs preliminary action by pre-storing only the essential base code and lifting function definitions in the lookup table, rather than pre-computing and storing all possible child codes. When a specific coding rate is needed, the system quickly generates the appropriate child code by applying the pre-stored lifting functions with the required parameters, achieving fast adaptation with minimal storage.
3Adaptability or versatility
If lifting operations with multiple parameters are performed, then code adaptability is improved, but computational complexity increases
Solution Approach 1:
The patent introduces dynamics by making the lifting parameters (circulant size, shift values, lifting function selection) adjustable based on the required coding rate and information length. The system dynamically selects and applies appropriate lifting parameters from the lookup table to generate child codes on-demand, allowing flexible adaptation without permanently configuring multiple code structures.
Solution Approach 2:
The patent uses copying by creating child codes as transformed copies of the base code through lifting operations. Instead of storing multiple independent code definitions, the system stores a single base code and generates copies with modified parameters (shifts, circulant sizes) as needed. This copying approach reduces computational complexity by reusing the base code structure while only modifying specific parameters.
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.