Heterogeneous Polar Code Kernels for Flexible Rate Matching
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Solution Overview
Problem
Existing polar codes are limited to binary symbol alphabets and restrict codeword lengths to powers of two, making it challenging to match coding rates required in communication systems, especially when the desired codeword length does not align with the power of two constraint.
Innovation Solution
The use of general polar codes that encode symbols of a q-ary alphabet, employing Kronecker product matrices and kernels like Reed-Solomon (RS) based kernels, allows for flexible codeword lengths and coding rates by implementing rate matching through puncturing or padding, enabling codewords of lengths other than powers of two.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If binary polar codes with power-of-two codeword lengths are used, then the coding structure is simple and well-defined, but the coding rate cannot be flexibly matched to communication system requirements
Solution Approach 1:
The patent changes the fundamental parameters of polar codes from binary (q=2) to q-ary alphabets with varying sizes (q=4, 8, 16, etc.), enabling codeword lengths to be any integer value rather than restricted to powers of two. This parameter change allows flexible rate matching while maintaining manageable code structure through systematic construction methods.
Solution Approach 2:
The patent segments the encoding process into multiple stages using different kernel sizes. By combining kernels of different sizes (e.g., 4-ary, 8-ary, 16-ary kernels) in a structured sequence, the system achieves flexible codeword lengths while keeping each individual kernel operation relatively simple and systematic.
2Adaptability or versatility
If general q-ary polar codes with flexible codeword lengths are implemented, then rate matching flexibility is improved, but decoder implementation complexity increases
Solution Approach 1:
The decoding process is segmented into multiple stages corresponding to the encoding stages, with each stage using kernels of matching sizes. This segmented approach allows the decoder to process different segments independently and systematically, reducing overall implementation complexity despite the flexible codeword lengths.
Solution Approach 2:
The patent develops a universal decoder architecture that can handle multiple kernel sizes (4-ary, 8-ary, 16-ary, etc.) through a unified processing framework. This multi-functional decoder design reduces implementation complexity by avoiding the need for separate decoders for each kernel size, while still supporting flexible codeword lengths.
3Manufacturing precision
If heterogeneous kernels of different sizes are combined, then rate matching precision is improved, but encoding complexity increases
Solution Approach 1:
The patent systematically varies the kernel size parameter (q) across different encoding stages to achieve precise rate matching. By changing the alphabet size parameter from 2 to 4, 8, 16, or other values in a controlled manner, the system achieves precise control over codeword length and coding rate while maintaining systematic encoding procedures.
Solution Approach 2:
The encoding structure dynamically adapts by selecting different kernel sizes at different stages based on the desired codeword length and coding rate. This dynamic selection of kernel parameters allows precise rate matching while keeping the overall encoding process systematic and manageable through clear selection rules.
Data Source
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AI summary
Systems and methods are disclosed for performing rate matching when using general polar codes. In one embodiment, a method of generating a codeword includes receiving bits at a polar encoder and encoding the bits using polar encoder kernels. The polar encoder kernels include a first kernel and a second kernel. The first kernel receives a set of input q-ary symbols and modifies the set of input q-ary symbols according to a first kernel generator matrix to produce a set of output q-ary symbols. The second kernel receives a set of input l-ary symbols, where l does not equal q, and modifies the set of input l-ary symbols according to a second kernel generator matrix to produce a set of output l-ary symbols. For example, the first kernel may be a binary kernel and the second kernel may be a Reed-Solomon (RS) based kernel.