Polar Code Frozen-Bit Layout for Low-Latency Automorphism Decoding
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Solution Overview
Problem
Current polar code decoding algorithms suffer from high latency due to their successive nature, and the automorphism group of polar codes has not been effectively utilized in decoding processes due to incomplete knowledge of its nature.
Innovation Solution
Designing polar codes with frozen bits that support automorphisms based on a binary upper triangular matrix, allowing for efficient automorphism-based decoding with reduced latency and improved Block Error Rate (BLER) performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If successive cancellation decoding algorithm is used for polar code decoding, then decoding performance is improved, but decoding latency increases
Solution Approach 1:
The patent segments the decoding process by dividing the codeword into multiple parts that can be decoded in parallel. Instead of processing bits sequentially as in traditional SC decoding, the invention partitions the decoding task into independent segments that can be handled simultaneously, thereby reducing overall decoding latency while maintaining acceptable performance
Solution Approach 2:
The patent performs preliminary actions by pre-calculating and storing certain decoding metrics and channel reliability information before the actual decoding process. This preprocessing enables faster decision-making during decoding, reducing the time required for each decoding step without sacrificing accuracy
2Loss of time
If automorphism-based decoding is applied to polar codes, then decoding latency is reduced, but the complexity of understanding and implementing the automorphism group increases
Solution Approach 1:
The patent develops a universal framework for applying automorphism-based decoding to polar codes that can handle different code lengths and rates. The invention creates a multi-functional decoding architecture that can accommodate various polar code configurations through a single unified approach, reducing the need for specialized implementations for each case
Solution Approach 2:
The patent utilizes parameter changes by transforming the polar code representation and exploiting changes in code parameters to enable efficient automorphism-based decoding. By adjusting and exploiting different parameter representations, the invention simplifies the implementation complexity while maintaining the latency reduction benefits of automorphism-based approaches
3Productivity
If frozen bits are configured to support automorphisms, then the number of automorphisms increases and decoding efficiency improves, but the flexibility in code design is reduced
Solution Approach 1:
The patent introduces asymmetry in the frozen bit configuration to support automorphisms. By deliberately creating asymmetric patterns in the frozen bit positions, the invention enables the code to possess automorphism properties that can be exploited for efficient decoding, while the asymmetric structure itself becomes the enabling feature rather than a limitation
4Productivity
If automorphism group knowledge is expanded for polar codes, then more efficient decoding algorithms can be developed, but the current incomplete knowledge limits immediate application
Solution Approach 1:
The patent performs preliminary research and characterization of the automorphism group of polar codes, establishing a foundation of knowledge that enables future efficient decoding algorithms. By conducting this preliminary analysis now, the invention creates a knowledge base that will support more advanced decoding techniques in the future, even though complete knowledge is not yet achieved
Data Source
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AI summary
The present disclosure relates generally to the field of data encoding and decoding, and particularly to automorphism-based polar encoding and decoding apparatuses and methods, as well as computer program products embodying the method steps in the form of computer codes. More specifically, it is proposed to design polar codes such that their frozen bits support automorphisms described by a binary upper triangular matrix having a diagonal including at least one of zeros and units. Codewords generated using these polar codes may be subsequently subjected to automorphism-based polar decoding in an efficient manner and with a lower decoding latency compared to the conventional Successive Cancellation List decoding algorithms. Furthermore, the efficiency of the automorphism-based polar decoding may be increased even more if the automorphisms are based on matrix elements arranged above the diagonal in a vicinity of a bottom right corner of the binary upper triangular matrix.