Systematic Polar Encoding With Data Checks and Puncturing
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Solution Overview
Problem
Existing systematic encoding methods for polar codes are not compatible with data-checks and puncturing methods, leading to performance penalties and inapplicability of existing systematic encoding techniques, which hinders the maximization of channel capacity and noise immunity while maintaining low computation complexity.
Innovation Solution
A systematic polar encoder is developed that includes a data mapper and a non-systematic polar encoder with data checks, using a transform matrix G and input/output partitions to ensure that the data word is transparently included in the codeword, and puncturing is applied to adjust the codeword length, while maintaining low complexity through specific design rules for the transform matrix and partitions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing systematic encoding methods are used for polar codes, then encoding can be performed, but they are not compatible with data-checks and puncturing methods, leading to performance penalties and inapplicability
Solution Approach 1:
The transform input word u is segmented into four distinct parts: uF (fixed part independent of data), uT (inverse puncture word), uI (carrying modified data), and uC (carrying check word). This segmentation allows each part to be independently optimized for its specific function, enabling compatibility with data-checks and puncturing while maintaining systematic encoding properties. The fixed part uF contains frozen bits that are independent of the data word, while uI carries the actual data information, creating a structure that naturally accommodates both systematic and non-systematic requirements.
Solution Approach 2:
A data mapper is introduced as an intermediary component that transforms the original data word d into a modified data word d' before encoding. This data mapper acts as a mediator between the systematic encoding requirement and the data-checks/puncturing methodology, converting input data in a way that enables compatibility with both approaches without sacrificing error correction performance or systematic properties.
2Reliability
If channel capacity is maximized using polar codes, then noise immunity improves, but computation complexity increases
Solution Approach 1:
Different parts of the transform input word u are assigned different qualities and functions: uF contains frozen bits that are completely fixed and require no computation, uT contains inverse puncture words that are predetermined, uI carries modified data that requires systematic encoding, and uC carries check words that provide error detection capability. This local differentiation allows the encoder to achieve high noise immunity through proper channel polarization while keeping computation complexity low by avoiding full systematic encoding of all bits.
3Ease of operation
If systematic encoding is implemented to include data word transparently in codeword, then data recovery is simplified, but compatibility with data-checks and puncturing is lost
Solution Approach 1:
The code structure is segmented such that the codeword contains both systematic parts (where data bits appear transparently) and non-systematic parts (where check bits and punctured bits are located). Specifically, certain positions in the codeword directly correspond to data bits from the modified data word d’, providing systematic properties for easy recovery, while other positions accommodate check words and punctured bits, maintaining compatibility with advanced error correction methodologies.
Solution Approach 2:
The polar code encoder is designed with universal properties that allow it to perform multiple functions: it can operate in systematic mode where data bits are transparently included for simple recovery, and simultaneously accommodate data-checks and puncturing for enhanced error correction performance. The transform matrix G and the partitioning scheme enable the same encoding structure to serve both systematic and non-systematic requirements, making the system multi-functional and adaptable to different operational modes.
Data Source
AI summary
A systematic polar encoder with data checks includes a data mapper receiving input data containing information to be polar coded for transmission and generating modified data, and a nonsystematic polar encoder implementing a transform matrix encoding the modified data to produce a codeword x such that, for some sub-sequence of coordinates S, xS=d. For nonsystematic encoding, a transform input u includes first and second parts for words independent of the data, the second part for an inverse puncture word, a third part carrying the modified data, and a non-null part carrying a check word derived from the modified data. A transform output includes a punctured part for a puncture word, a part carrying the data, and a part serving as redundant symbols, with the codeword x related to the transform output by x=zQ where Q is the complement of the punctured part P.