Polar Code Parity Bit Mapping by Row-Weight Sub-Channel Selection
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Solution Overview
Problem
Existing polar coding techniques face inefficiencies in selecting sub-channels for parity bits during encoding, leading to suboptimal performance in error correction and detection, particularly due to the reliance on polarization reliability metrics alone.
Innovation Solution
The method involves selecting sub-channels for parity bits based on a combination of polarization reliability metrics and hamming weights, reserving specific sub-channels with minimal or twice the minimal row weights, and using a cyclic shift register to determine parity bit values, thereby improving the distribution and reliability of parity bits across sub-channels.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If sub-channels are selected for parity bits based solely on polarization reliability metrics, then the encoding process is simple, but the error correction performance is suboptimal
Solution Approach 1:
The patent changes the selection criteria parameter from using only polarization reliability metrics to using a combination of polarization reliability metrics and row weights of the Kronecker matrix. This parameter change enables better error correction performance by considering both the reliability of sub-channels and their structural properties in the polar code construction.
Solution Approach 2:
The patent segments the sub-channels into different groups based on their row weights (e.g., minimum row weight, twice the minimum row weight). This segmentation allows systematic selection of parity bit positions by categorizing sub-channels according to their structural characteristics, improving both performance and selection efficiency.
2Reliability
If parity bits are placed in sub-channels with minimal row weights, then decoding probability improves, but the distribution of parity bits becomes less uniform
Solution Approach 1:
The patent applies local quality by differentiating the treatment of sub-channels based on their local properties (row weights). Instead of uniform distribution, parity bits are strategically placed in sub-channels with specific row weight characteristics (minimum, twice minimum), creating non-uniform but optimized distribution that improves decoding probability while maintaining controlled uniformity through systematic selection.
3Reliability
If more sub-channels are selected for parity bits from the reliable segment, then error detection capability improves, but latency increases
Solution Approach 1:
The patent applies partial action by selecting a specific number of sub-channels for parity bits based on predetermined criteria (minimum row weight, twice minimum row weight) rather than using all available sub-channels. This partial selection achieves sufficient error detection capability while avoiding the latency penalty of processing excessive numbers of parity bit positions.
Data Source
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AI summary
Embodiment techniques map parity bits to sub-channels based on their row weights. The row weight for a sub-channel may be viewed as the number of "ones" in the corresponding row of the Kronecker matrix or as a power of 2 with the exponent (i.e. the hamming weight) being the number of "ones" in the binary representation of the sub-channel index (further described below). In one embodiment， candidate sub-channels that have certain row weight values are reserved for parity bit (s). Thereafter, K information bits may be mapped to the K most reliable remaining sub-channels, and a number of frozen bits (e.g. N-K) may be mapped to the least reliable remaining sub-channels. Parity bits may then mapped to the candidate sub-channels, and parity bit values are determined based on a function of the information bits.