Polar Code Construction for Non-Power-of-Two Block Sizes
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Solution Overview
Problem
FRANK polar code construction in wireless communication systems faces challenges due to insufficient polarization of bit-channels when the block size is not a power of two, leading to unreliable bit-channel selection and decreased performance in achieving the desired signal-to-noise ratio (SNR) for a given block error probability.
Innovation Solution
The implementation of enhanced FRANK polar code construction, which applies a capacity backoff to identify and allocate information bits to the most reliable bit-channels by recursively determining the number of polarized channels and using a capacity backoff function to ensure sufficient polarization, thereby improving bit-channel reliability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the block size is rounded up to the nearest power of two for polar code encoding, then the code can be generated using standard polar code construction, but excess bits must be punctured which affects bit-channel polarization and reduces reliability
Solution Approach 1:
The polar code construction is divided into multiple stages of polarization, with each stage processing subsets of bit-channels. This segmentation allows the system to handle punctured bits at specific stages rather than uniformly across all bit-channels, preserving reliability while maintaining ease of generation through structured processing.
Solution Approach 2:
Different bit-channel subsets receive different treatment based on their polarization characteristics. The method identifies and separates bit-channels affected by puncturing from those that are not, applying localized polarization processing to each group. This ensures that unpunctured bit-channels achieve full polarization while punctured bit-channels are handled appropriately for their reduced reliability.
2Productivity
If punctured bits are removed to achieve the desired block size, then the correct number of information bits are transmitted, but the polarization of bit-channels is disrupted and selection of reliable bit-channels becomes difficult
Solution Approach 1:
The method performs preliminary identification of which bit-channels will be punctured before the actual encoding process. This advance knowledge allows the polarization process to be structured in advance to account for upcoming puncturing, ensuring that the most reliable bit-channels are selected for information bits even before puncturing occurs.
Solution Approach 2:
The system uses feedback from the puncturing pattern to adjust the polarization process. By monitoring which bits will be punctured and how this affects overall code structure, the method dynamically adjusts bit-channel selection and polarization staging to maintain reliability despite the removal of excess bits.
3Device complexity
If standard FRANK polar code construction is used without modification, then the implementation is simple and fast, but it cannot achieve sufficient polarization for non-power-of-two block sizes
Solution Approach 1:
The polarization process is made dynamic by introducing multiple stages that can be selectively applied based on the specific block size and puncturing pattern. Rather than a fixed single-stage polarization, the system adapts the number and structure of polarization stages to match the requirements of non-power-of-two block sizes, maintaining both simplicity and sufficiency.
Data Source
AI summary
Methods, systems, and devices for wireless communications are described. An encoder of a wireless device may receive a number of information bits and a block size for transmission. If the block size is not a power of two, the encoder may round the block size up to the nearest power of 2, generate a larger codeword, and puncture the excess bits. The punctured bits may affect a rate of polarization when generating a polar code, and sub-blocks with a high number of punctured bits may produce too few sufficiently polarized channels. The encoder may implement a capacity backoff when polar coding to identify a greater number of polarized channels. The encoder may assign information bits to sufficiently polarized channels of the greater number of polarized channels.