Polar Code Parity Check Bit Placement for Reliable List Decoding
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Solution Overview
Problem
Polar codes in wireless communication struggle with rate loss due to assigning zeros at indices where virtual sub-channels are not fully polarized, leading to suboptimal error-correcting performance.
Innovation Solution
Assign parity check bits to indices where zeros would otherwise be placed, improving error-correcting performance by spreading message bits over multiple virtual sub-channels.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If zeros are assigned to message indices not among the most-reliable set, then device complexity is reduced, but error-correcting performance deteriorates
Solution Approach 1:
The patent changes the parameter assignment by assigning parity check bits to indices where zeros would otherwise be placed. Specifically, parity check bits are assigned to indices in the range [K, K+nPC-1] where nPC is the number of parity check bits, instead of assigning zeros to these indices. This parameter change allows the system to maintain simple encoding operations while improving error-correcting performance through better utilization of virtual sub-channels.
2Reliability
If parity check bits are assigned to indices where zeros would otherwise be placed, then error-correcting performance is improved, but device complexity increases
Solution Approach 1:
The patent implements parameter changes by modifying the index assignment for parity check bits. The parity check bits are generated based on message bits and assigned to specific indices [K, K+nPC-1] among the most-reliable set. This systematic parameter assignment improves error-correcting performance while maintaining manageable encoding complexity through structured bit placement.
Solution Approach 2:
The patent introduces parity check bits as an intermediary element that mediates between message bits and the encoding process. These parity check bits are generated from message bits using systematic rules and placed at specific indices to provide error-detection and correction capabilities, thereby improving reliability without requiring complete redesign of the encoding system.
3Reliability
If message bits are spread over multiple virtual sub-channels, then error-correcting performance is improved, but information transmission efficiency decreases
Solution Approach 1:
The patent optimizes parameter assignment by carefully selecting which indices receive parity check bits versus message bits. The system assigns parity check bits to indices [K, K+nPC-1] among the most-reliable set, while message bits are assigned to remaining indices. This parameter optimization spreads message bits across multiple virtual sub-channels for improved error correction while minimizing the impact on transmission efficiency through systematic index selection.
Data Source
AI summary
Error-correcting performance of polar codes is improved by assigning parity check bits to small, reliable indices. Zeros are assigned to message indices not among a most-reliable set of the message indices, information bits and parity check bits are assigned to the most-reliable set of the message indices, with the parity check bits generated on the information bits assigned to the smallest of the most-reliable set and then assigned to the smallest indices of the most-reliable set that follow the information bits on which the parity check pits are generated. During successive cancellation list decoding, the parity check bits allow error events to be promptly corrected during decoding.