LDPC Lifting Table Selection 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 suboptimal performance and resource inefficiency.
Innovation Solution
The method involves determining a circulant size, lifting function, and labelled base matrix Parity Check Matrix (PCM) using a lifting table to derive a child PCM for encoding and decoding, allowing for adaptive coding rates and lengths by switching between different labelled PCMs, and storing these parameters in a lifting table for efficient resource allocation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If quasi-cyclic LDPC coding systems are used to achieve reliable data transmission, then error correction capability is improved, but hardware resource consumption increases
Solution Approach 1:
The parity check matrix is segmented into multiple labelled base PCMs, each representing a specific code rate and information length combination. This segmentation allows the system to use only the necessary segment (labelled PCM) for a given transmission scenario, reducing hardware resource consumption while maintaining error correction capability through the structured design of each base PCM.
Solution Approach 2:
The system changes parameters (circulant size, lifting function, base PCM selection) based on the specific transmission requirements of information length and code rate. By pre-defining multiple labelled base PCMs with different parameters and selecting the appropriate one for each scenario, the system achieves optimal error correction performance while minimizing hardware resources for the specific operating conditions.
2Adaptability or versatility
If multiple code rates and information lengths are supported to improve adaptability, then system versatility is improved, but device complexity increases
Solution Approach 1:
Each labelled base PCM is designed to serve multiple functions by supporting specific combinations of code rates and information lengths. The lifting function and circulant size parameters enable the same base PCM structure to be adapted for different coding scenarios, allowing a single hardware implementation to handle multiple code rates and information lengths without requiring separate dedicated structures for each case.
Solution Approach 2:
Multiple labelled base PCMs are pre-defined and stored in a lifting table during system initialization, with each labelled PCM optimized for specific code rate and information length combinations. When transmission begins, the system quickly selects the appropriate pre-defined labelled PCM from the table based on the required parameters, avoiding the need to generate or switch complex structures during actual data transmission, thus reducing real-time computational complexity.
3Adaptability or versatility
If lifting tables with multiple combinations are stored to enable flexible coding, then adaptability is improved, but storage requirements increase
Solution Approach 1:
The lifting table is organized with local quality by creating distinct entries (labelled base PCMs) for specific combinations of code rates and information lengths rather than storing all possible combinations uniformly. Each labelled PCM contains only the parameters and structures necessary for its specific intended use case, allowing the system to store a manageable set of specialized configurations that can be efficiently selected based on the specific transmission requirements.
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.