LDGC Generator Matrix Encoding With Triangular Systematic Structure
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Solution Overview
Problem
Existing FEC encoding methods, such as LT codes and Raptor codes, face high encoding complexity due to the lack of support for systematic codes and the need for precoding procedures, which complicates their application in error detection and correction, especially in point-to-multipoint services like data broadcasting.
Innovation Solution
The method involves constructing a Low Density Generator Matrix Code (LDGC) with specific triangular matrix structures to encode information bits efficiently, reducing encoding complexity by using a generator matrix that supports systematic codes without the need for additional precoding, similar to the degree distribution principle of LT codes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If LT codes are used for encoding, then linear encoding and decoding time is achieved, but systematic codes are not supported making it difficult to meet practical FEC encoding requirements
Solution Approach 1:
The generator matrix is segmented into two parts: an identity matrix portion and a parity matrix portion. This segmentation allows the code to maintain systematic structure while achieving efficient encoding, resolving the contradiction between encoding speed and systematic code support.
2Adaptability or versatility
If Raptor codes are used for encoding, then systematic codes are supported, but a separate precoding procedure is needed leading to higher encoding complexity
Solution Approach 1:
The precoding operation and main encoding operation are merged into a single matrix multiplication process. By incorporating the precoding function directly into the generator matrix structure, the patent eliminates the need for separate precoding procedures, thereby reducing encoding complexity while maintaining systematic code support.
3Reliability
If traditional FEC codes like RS codes are used, then error detection and correction are implemented, but encoding and decoding complexity is high limiting application to short codes
Solution Approach 1:
The patent changes the structural parameters of the generator matrix to a sparse low-density form with specific triangular structure. This parameter change enables efficient Gaussian elimination-based encoding and decoding operations, reducing computational complexity while maintaining error detection and correction capabilities for longer code lengths.
Data Source
AI summary
A method and system for encoding the low density generator matrix code are disclosed. The encoding method includes the following steps: S102, constructing a generator matrix Gldgc with L rows and N+L−K columns, wherein a phalanx Gldgc(1:L, 1:L) which consists of L rows and the first L columns of the generator matrix Gldgc is an upper triangular matrix or a lower triangular matrix, the K, L and N being positive integers, and K<L<N; S104, adding L−K known bits to the K-length information bit sequence that needs to be encoded to generate an information bit sequence m which has a length of L; S106, according to I×Gldgc(1:L, 1:L)=m, using the phalanx Gldgc(1:L, 1:L) which consists of L rows and the first L columns of the generator matrix Gldgc and the information bit sequence m which has a length of L, to generate an intermediate variable I, and according to C=I×Gldgc, using the generator matrix Gldgc to encode an intermediate variable I, to generate an encoding sequence which has a length of N+L−K; and S108, deleting L−K known bits from the encoding sequence which has a length of N+L−K, to generate an encoding sequence which has a length of N.