Punctured Polar Encoding for Flexible Codeword Length Matching
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Solution Overview
Problem
Polar codes, particularly binary polar codes, face limitations in coding rate matching due to restrictions on codeword length, which can lead to suboptimal performance in error correction and decoding complexity, especially when the required codeword length does not align with the power-of-two constraint.
Innovation Solution
The implementation of non-binary general polar codes, such as Reed-Solomon (RS) based codes, which allow for codeword lengths that are not restricted to powers of two, enabling flexible rate matching through puncturing or padding to achieve desired coding rates while reducing decoding complexity and improving error correction performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If binary polar codes with power-of-two codeword length constraint are used, then the encoding structure is simple and well-defined, but the coding rate matching flexibility is limited and error correction performance is suboptimal when required codeword length does not align with power-of-two
Solution Approach 1:
The patent changes the fundamental parameter of codeword length from power-of-two constraints to arbitrary lengths. By using general polar codes constructed from kernels of size m×m where m≥2 (not necessarily a power of two), the system can accommodate any codeword length N that is a multiple of m^l, providing flexible rate matching while maintaining structured encoding
Solution Approach 2:
The patent introduces dynamic adaptability in codeword length selection. The encoder can dynamically choose different codeword lengths based on the required coding rate and transmission conditions, rather than being fixed to power-of-two lengths. This is achieved through puncturing or extending the base codeword of length N to achieve the desired effective codeword length M
2Adaptability or versatility
If puncturing is applied to achieve desired coding rates, then coding rate matching flexibility is improved, but frame error rate increases if punctured bits are not properly selected
Solution Approach 1:
The patent applies preliminary action by pre-determining the optimal puncturing pattern before actual transmission. The encoder selects which bits to puncture based on their reliability information (such as channel polarization properties) in advance, ensuring that only less reliable bits are removed. This preliminary selection minimizes the impact on error correction performance while achieving the desired coding rate
Solution Approach 2:
The patent applies local quality by treating different bit positions differently during puncturing. Instead of uniformly puncturing bits, the system identifies specific bit positions with lower reliability (based on channel polarization) and selectively punctures those positions. This localized approach preserves the most reliable bits, maintaining lower frame error rates while achieving rate matching
Data Source
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AI summary
Systems and methods are disclosed that relate to performing rate matching when using polar codes. In one embodiment, a plurality of bits are received at a polar encoder. A value is obtained that corresponds to at least one of: a coding rate to be used to transmit the plurality of bits, and a number of coded bits to be used to transmit the plurality of bits. It is determined which range of values the value falls within, and an information sequence is obtained that corresponds to the range the value falls within. The plurality of bits are mapped to a subset of positions of an input vector according to the information sequence. The remaining positions of the input vector are set as frozen values that are known by a decoder. The input vector is then encoded in the polar encoder to generate a codeword.