Multilevel Polar Coding for Higher-Order Modulation Error Balancing
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Solution Overview
Problem
Extending polar codes to systems using higher-order modulation techniques is challenging due to output bits experiencing different effective channels, making standard polar code design techniques not generally applicable.
Innovation Solution
Implementing multilevel coding (MLC) with binary alphabet polar codes, where different bit levels are associated with specific coding rates and symbol mapping rules to ensure equal error rates across bit levels, using techniques like successive cancellation decoding and specially designed symbol mappings.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If polar codes are extended to higher-order modulation techniques, then channel capacity utilization is improved, but output bits experience different effective channels making standard design techniques inapplicable
Solution Approach 1:
The patent segments the coding process into multiple levels, with each level handling different bit positions. The first level uses a first binary alphabet polar code with a first coding rate, while the second level uses a second binary alphabet polar code with a second coding rate. This segmentation allows each level to be optimized independently for its specific requirements, resolving the contradiction between achieving high channel capacity utilization and maintaining manageable design complexity.
2Reliability
If different coding rates are used at different bit levels, then error rate equalization is achieved, but encoding and decoding complexity increases
Solution Approach 1:
The patent applies local quality by assigning different coding rates to different bit levels based on their specific error rate requirements. The first binary alphabet polar code uses a first coding rate optimized for the first bit level, while the second binary alphabet polar code uses a second coding rate optimized for the second bit level. This localized optimization achieves error rate equalization across all bit levels while keeping each individual coding operation relatively simple.
Data Source
AI summary
A method includes receiving multiple bits to be transmitted. The method also includes applying a first binary alphabet polar code to a first subset of the multiple bits to generate first encoded bits. The first encoded bits are associated with a first bit level of a multilevel coding scheme. The method further includes generating one or more symbols using the first encoded bits and bits associated with a second bit level of the multilevel coding scheme. The first binary alphabet polar code is associated with a first coding rate. In addition, the method could include applying a second binary alphabet polar code to a second subset of the multiple bits to generate second encoded bits. The second encoded bits are associated with the second bit level. The second binary alphabet polar code is associated with a second coding rate such that the bit levels have substantially equal error rates.