LDGC Generator Matrix Expansion for Variable-Length Systematic Encoding
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Solution Overview
Problem
Existing Low Density Generator Matrix Codes (LDGC) face limitations in encoding complexity and flexibility, particularly in supporting systematic codes and varying code lengths, which hinders their application in error correction for data transmission.
Innovation Solution
The method involves constructing a uniform basic matrix for LDGC, modifying and expanding it to generate a generator matrix suitable for different code lengths, allowing for efficient encoding and decoding by using an intermediate variant and expanding factors, thereby reducing encoding and decoding complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional FEC codes (RS codes, Fountain codes) are used to ensure reliable transmission in point-to-multipoint services, then error correction capability is improved, but encoding and decoding complexity increases substantially
Solution Approach 1:
The code is segmented into information bits and parity bits through systematic encoding structure. The generator matrix is divided into sub-matrices with specific structures (upper triangular or lower triangular) that enable efficient computation. This segmentation allows the encoding process to be broken down into manageable matrix operations rather than complex polynomial computations required by conventional codes.
Solution Approach 2:
The patent changes the fundamental parameters of the code structure by using a generator matrix with sparse nonzero elements and specific triangular sub-matrix structures. This parameter change transforms the encoding complexity from polynomial-based (high complexity) to matrix-based (lower complexity) operations, while maintaining the error correction capability through the same FEC principles.
2Productivity
If Raptor codes with pre-coding technique are used to achieve higher decoding efficiency, then decoding performance is improved, but encoding complexity increases due to separate pre-coding process and pre-coding matrix requirements
Solution Approach 1:
The patent merges the pre-coding function into the main encoding process by incorporating the triangular sub-matrix structure directly into the generator matrix. This eliminates the need for a separate pre-coding stage and pre-coding matrix, combining multiple functions into a single encoding operation that achieves both efficiency and simplicity.
Solution Approach 2:
The generator matrix structure with triangular sub-matrices serves multiple functions simultaneously: it enables systematic encoding, provides efficient decoding through backward/forward substitution, and supports variable code lengths. This multi-functionality eliminates the need for separate pre-coding processes required by Raptor codes.
3Device complexity
If LT codes are used to achieve linear encoding and decoding time, then encoding complexity is reduced, but the ability to support systematic codes is lost
Solution Approach 1:
The patent applies local quality by creating specific structural properties in different parts of the generator matrix. The upper triangular or lower triangular sub-matrices provide systematic encoding capability in specific regions, while the sparse nonzero elements provide efficient computation elsewhere. This localized structural design enables both systematic support and low complexity.
4Productivity
If LDGC with fixed generator matrix is used to achieve low encoding complexity, then encoding efficiency is improved, but flexibility in supporting various code lengths is reduced
Solution Approach 1:
The patent introduces dynamics by making the generator matrix adaptable to different code lengths through the use of triangular sub-matrices with variable dimensions. The matrix structure can be adjusted dynamically based on the required code length and rate, allowing the same encoding algorithm to efficiently handle various coding scenarios without sacrificing performance.
Data Source
AI summary
An encoding method, encoding device, decoding method and decoding device for low density generator matrix codes (LDGC) are disclosed. Wherein, the encoding method comprises: construct an LDGC mother code set using P LDGC with code rate R0 and different code lengths, wherein the LDGC mother code set has a uniform basic matrix Gbuniform wherein,R0=kbnb,kb denotes the number of rows and nb denotes the number of columns in the basic matrix; obtain length L of an intermediate variant according to length K of an information bit sequence to be encoded in the LDGC mother code set; modify and expand the basic matrix to obtain a generator matrix Gldgc using the length L of the intermediate variant and the number kb of rows in the basic matrix; and encode the information bit sequence to be encoded using a matrix Gldgc (1:L,1:N+L−K) composed of L rows and the front N+L−K columns of the generator matrix, wherein N denotes the length of the encoded information.