LDPC Sparse Graph Construction With Loop-Length-Aware PEG
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods face challenges in constructing sparse graph codes with optimal loop structures, leading to difficulties in achieving efficient encoding and decoding due to the creation of short loops and random node configurations, which result in decreased encoding efficiency and increased calculation complexity.
Innovation Solution
A modified progressive edge-growth (PEG) algorithm that selectively expands nodes to lengthen loops within the sparse graph, ensuring that the total number of edges and minimum loop length are maintained, allowing for local optimization and efficient encoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a sparse graph is constructed using conventional methods, then the graph can be created, but short loops are formed between arbitrary nodes leading to decreased encoding efficiency
Solution Approach 1:
The patent modifies the PEG algorithm by changing the node selection parameter - specifically selecting nodes that maximize loop length rather than selecting arbitrary nodes. This parameter change in the node selection criterion directly controls loop length and improves encoding efficiency by avoiding short loops.
Solution Approach 2:
The patent applies local optimization by modifying the node selection process to specifically address loop formation in local regions of the graph. By selecting nodes that maximize the length of loops formed with previously added nodes, the algorithm locally optimizes loop structure throughout the graph construction process.
2Ease of manufacture
If nodes are selected randomly in the PEG algorithm, then the construction process is simple, but short loops are created and encoding efficiency deteriorates
Solution Approach 1:
The patent changes the node selection parameter from random selection to selection based on loop length maximization. This parameter change maintains the iterative construction approach of PEG while improving reliability by systematically avoiding short loops that degrade encoding performance.
Solution Approach 2:
The modified algorithm incorporates feedback by evaluating the loop length that would be created by adding an edge between a new node and an existing node. This feedback mechanism guides node selection to maximize loop length, thereby improving encoding performance while maintaining construction simplicity.
3Productivity
If the sparse graph has optimal loop structure, then encoding efficiency is improved, but the construction complexity increases
Solution Approach 1:
The patent changes the node selection parameter to maximize loop length, which optimizes the loop structure during construction. This parameter change achieves optimal encoding efficiency without significantly increasing construction complexity because it uses a straightforward selection criterion based on loop length calculation.
Solution Approach 2:
The patent applies partial optimization by focusing only on the loop length parameter during node selection, rather than optimizing all graph properties simultaneously. This partial action approach achieves improved encoding efficiency through loop structure optimization without the complexity of comprehensive graph optimization.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
The purpose of the present invention is to efficiently create a sparse graph in a sparse graph code. The present invention relates to a selective PEG algorithm, creating a sparse matrix while maintaining row weight/column weight at arbitrary multi-levels, and in the process, inactivating an arbitrary edge so that a minimum loop formed between arbitrary nodes is enlarged or performing constrained interleaving, so that encoding efficiency in the case where a matrix space is narrow is improved.