Systematic Polar Encoding for Punctured Codes With CRC Checks
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Solution Overview
Problem
Current systematic encoding methods for polar codes are not compatible with data-checks and puncturing, leading to performance penalties and inapplicability of existing systematic encoding techniques, which hinders the exploitation of channel capacity and noise immunity while maintaining low computation complexity.
Innovation Solution
A systematic polar encoder is developed that partitions the input and output space of the polar transform matrix to enable puncturing, shortening, and CRC check attachment, allowing for low-complexity systematic encoding that maintains performance comparable to non-systematic encoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If systematic encoding is applied to polar codes, then BER performance is improved and channel capacity is better exploited, but existing systematic encoding methods become incompatible with data-checks and puncturing, leading to performance penalties
Solution Approach 1:
The encoder is divided into separate functional modules: a systematic polar code encoder that handles the polar coding operation, a puncturing module that selectively removes bits, and a CRC attachment module that appends check bits. This segmentation allows each module to perform its function independently, enabling systematic encoding to work seamlessly with both data-checks and puncturing operations without performance penalties.
Solution Approach 2:
The patent introduces an intermediary structure where the systematic polar code encoder produces an intermediate codeword that is then processed by subsequent modules for puncturing and CRC attachment. This intermediary approach allows the systematic encoding to be decoupled from the puncturing and check-bit attachment operations, resolving the compatibility issue while maintaining BER performance.
2Reliability
If higher complexity encoding schemes are used to reduce BER, then noise protection is improved, but computation complexity increases making them impractical for expected data transmission rates
Solution Approach 1:
The patent employs parameter changes by utilizing the structure of the polar transform matrix G and its properties to optimize the encoding process. By carefully selecting which bits to puncture and how to arrange the systematic bits, the encoder achieves strong noise protection with reduced computational complexity compared to exhaustive search methods.
Solution Approach 2:
The systematic polar code encoder performs preliminary encoding operations that prepare the data in a form that is optimized for subsequent puncturing and transmission. By pre-organizing the codeword structure with systematic bits in specific positions, the encoder reduces the computational burden during decoding while maintaining robust noise protection capabilities.
3Ease of manufacture
If non-systematic polar encoders are used, then implementation is simpler, but channel capacity exploitation and noise immunity are not fully achieved
Solution Approach 1:
The encoder architecture is segmented into distinct functional blocks that can be independently implemented and optimized. The systematic polar code encoder is separated from the puncturing and CRC attachment functions, allowing each component to be implemented using straightforward algorithms while collectively achieving superior channel capacity exploitation and noise immunity.
Solution Approach 2:
The systematic polar code encoder is designed with universal applicability, working effectively with various puncturing patterns and CRC configurations. This multi-functional design allows the same encoder structure to achieve both implementation simplicity and optimal channel capacity exploitation across different transmission scenarios.
Data Source
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AI summary
A systematic polar encoder 300, 500 with data checks includes a data mapper 310, 510, 700 receiving input data 301, 501 containing information for transmission and generating modified data 303, 503, and a nonsystematic polar encoder 320, 400, 520 implementing a transform matrix 600 encoding the modified data to produce a codeword x 302, 502 such that, for some sub-sequence of coordinates S, x s = d. For nonsystematic encoding, a transform input u 406, 601 includes parts for words independent of the data 403, for an inverse puncture word 405, for the modified data 303, 401, 503, and for carrying a check word 404 derived from the modified data. A transform output 407, 602 includes parts for a puncture word, for carrying the data, and for serving as redundant symbols, with codeword x related to transform output by x = z Q where Q is the complement of the punctured part.