Systematic TF Code Encoding Using Triangular Generator Factorization
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Solution Overview
Problem
There are no methods in prior art specifically designed for systematic encoding of Triangular Factorization (TF) codes or their embodiments, such as Polarization Adjusted Convolutional (PAC) codes, which are newer types of linear block codes, limiting the ability to reduce complexity and improve error correction performance.
Innovation Solution
The present disclosure provides systematic encoding methods for TF codes and PAC codes, utilizing triangular factorization of the generator matrix into outer and inner transform matrices, specifically an invertible upper-triangular (IUT) and invertible lower-triangular (ILT) matrix structure, to reduce complexity and improve error correction performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If systematic encoding methods are implemented for TF codes and PAC codes, then computational complexity is reduced and error correction performance is improved, but prior art lacked specific methods for these code types
Solution Approach 1:
The generator matrix is segmented into two triangular factors (upper triangular and lower triangular matrices), allowing the encoding process to be divided into two simpler sequential steps rather than one complex matrix multiplication, thereby reducing computational complexity while maintaining error correction capabilities
Solution Approach 2:
The invention changes the parameter representation by using triangular factorization of the generator matrix into specific upper and lower triangular forms, which enables more efficient systematic encoding operations and improves both computational complexity and error correction performance for TF codes and PAC codes
2Ease of operation
If non-systematic encoding is used, then the encoding process is simpler, but the source data block does not appear transparently as part of the transmitted code block and SER/BER performance degrades
Solution Approach 1:
The invention changes the encoding approach by using systematic encoding with triangular factorization, where the source data block appears transparently in the transmitted code block, improving SER/BER performance while maintaining practical encoding simplicity through the structured triangular matrix form
3Reliability
If systematic encoding is used to improve SER/BER performance, then the source data block appears transparently as part of the transmitted code block, but device complexity increases
Solution Approach 1:
The systematic encoding process is segmented into two simpler operations using triangular factorization, reducing the overall device complexity required to achieve improved SER/BER performance while maintaining the transparency of the source data block in the transmitted code block
Data Source
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AI summary
A systematic encoder 300 reliably transferring a source data block (SDB) 311 is configured for an outer transform matrix U and an inner transform matrix L. An inner encoder 301 receives the SDB and generates an output constraint block (OCB) 312 as an SDB image under an inverse of a submatrix of the inner transform matrix. An outer encoder 302 receives a fixed data block (FDB) 313 and the OCB and generates a transform output block (TOB) 315 as a transform input block (TIB) 314 image under the outer transform matrix. The TIB contains the FDB transparently in a sub-block of the TIB, and the TOB contains the OCB transparently in a sub-block of the TOB. The inner encoder receives the TOB and generates a transmitted code block (TCB), transparently containing the SDB in a sub-block therein.