Heterogeneous Polar Kernels for Flexible Codeword Rate Matching
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Solution Overview
Problem
Existing error control coding technologies, such as Arikan polar codes, are limited to binary symbol alphabets and restrict codeword lengths to powers of two, making it difficult to match coding rates with varying network conditions.
Innovation Solution
General polar codes that encode q-ary symbols, using both binary and Reed-Solomon (RS) based kernels to generate codewords of various sizes, allowing for rate matching through puncturing or padding to achieve desired coding rates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Arikan polar codes are used with binary symbol alphabet, then the coding structure is simple and well-defined, but the codeword length is restricted to powers of two which limits rate matching flexibility
Solution Approach 1:
The polar code construction is segmented into multiple stages with different kernel types. The first stage uses binary kernels (e.g., 2×2 or 4×4) to process binary symbols, while the second stage uses non-binary kernels (e.g., 8×8 Reed-Solomon based) to process q-ary symbols. This segmentation allows the system to achieve flexible code lengths and rates by combining different kernel operations, resolving the contradiction between adaptability and complexity.
Solution Approach 2:
The patent employs a composite kernel structure that combines binary and non-binary kernels in a unified polar code framework. The generator matrix is constructed as a composite of binary kernel matrices and non-binary kernel matrices, enabling the code to achieve both the simplicity of binary operations and the flexibility of non-binary operations for rate matching.
2Adaptability or versatility
If codeword length is restricted to powers of two, then the encoding process is straightforward, but the coding rate cannot be adjusted to match varying network conditions
Solution Approach 1:
The polar code system implements dynamic kernel selection where the choice of kernel size and type (binary vs. non-binary) is dynamically adjusted based on the desired coding rate and code length requirements. This allows the encoder to adapt to varying network conditions while maintaining operational simplicity through automated kernel selection based on predefined criteria.
3Productivity
If only binary kernels are used, then the implementation is simple and standardized, but the decoding throughput is limited for high-rate applications
Solution Approach 1:
The patent changes the parameter of kernel algebraic structure from purely binary to a combination of binary and non-binary (q-ary) structures. This parameter change enables the decoder to process more symbols per operation in non-binary kernels, increasing decoding throughput for high-rate applications while managing complexity through structured kernel designs that leverage efficient algebraic operations.
Data Source
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.