Polar Code Generator Matrix Layout for Low-Delay Decoding
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Solution Overview
Problem
Current polar code decoding methods face challenges in balancing decoding delay and performance, with sequential decoding experiencing high delay and non-sequential decoding compromising on performance due to mismatch with polar code design.
Innovation Solution
The proposed method employs a generator matrix with block upper or lower triangular structures, coupling multiple short codes to reduce encoding and decoding complexity while improving performance by using submatrices strategically located on the diagonal, allowing for efficient encoding and decoding of polar codes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If polar code sequential decoding is used, then compatibility with polar code design and convenience for theoretical analysis are improved, but decoding delay increases
Solution Approach 1:
The patent segments the polar code into multiple sub-blocks and processes them in parallel using a tree structure. Each sub-block can be decoded independently or with minimal interaction, allowing simultaneous processing of multiple segments rather than strict sequential bit-by-bit decoding. This reduces overall decoding delay while maintaining compatibility with polar code design principles.
Solution Approach 2:
The patent introduces a tree-based decoding structure that adds a dimensional aspect to the decoding process. Instead of a single sequential path, the decoding occurs across multiple parallel paths in a tree structure, enabling non-sequential processing while preserving the underlying polar code design compatibility.
2Loss of time
If polar code non-sequential decoding is used, then decoding delay is reduced, but decoding performance deteriorates due to mismatch with polar code design
Solution Approach 1:
By dividing the polar code into sub-blocks that can be processed in parallel, the patent achieves non-sequential decoding with reduced delay. The segmentation is designed to maintain the essential polar code structure within each sub-block, preserving decoding performance while enabling parallel processing.
Solution Approach 2:
The patent employs a nested structure where sub-blocks are organized within a tree hierarchy. Each level of the tree contains nested sub-blocks that can be processed at different granularities, allowing flexible parallel processing while maintaining the overall polar code structure and performance characteristics.
3Device complexity
If a block upper or lower triangular generator matrix with submatrices on diagonal is used, then encoding and decoding complexity is reduced, but encoding and decoding performance may be compromised
Solution Approach 1:
The generator matrix is segmented into block upper or lower triangular form with submatrices on the diagonal. This segmentation allows encoding and decoding to be performed on smaller, independent blocks rather than the entire code at once, significantly reducing computational complexity while maintaining overall code performance through proper sub-block design.
Solution Approach 2:
The patent employs dynamic selection between block upper triangular and block lower triangular generator matrix forms depending on the specific coding requirements. This dynamic approach allows optimization for different scenarios, balancing complexity reduction with performance maintenance by selecting the appropriate matrix structure.
Data Source
AI summary
A sending device may obtain a first to-be-encoded vector. The sending device may perform first encoding on the first to-be-encoded vector, to obtain a second to-be-encoded vector. The sending device may encode the second to-be-encoded vector based on a first generator matrix, to obtain an encoded codeword. The first generator matrix may include at least N+1 submatrices a, and N of the submatrices a may be located on a main diagonal of the first generator matrix. The first generator matrix may be a block upper triangular matrix, or the first generator matrix may be a block lower triangular matrix. The submatrix a is a polar kernel matrix with a size of 2m*2m, m is a natural number, and N is a natural number. The sending device may send the encoded codeword.