Twisted Polar Code Decoding with Fewer Iterations
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Solution Overview
Problem
Existing polar codes have a low error correction capability due to small minimum distance, leading to higher error probabilities in the waterfall region and saturation levels compared to LDPC and turbo codes.
Innovation Solution
The introduction of twisted polar codes with dynamic freezing and specific permutation structures, along with a successive cancellation decoding method that uses a heuristic function to reduce decoding complexity and iterations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If classical polar codes are used, then the encoding and decoding structure is simple, but the error correction capability is poor due to small minimum distance
Solution Approach 1:
The code construction is segmented into multiple layers (m layers) where each layer applies a specific transformation matrix. This multi-layer segmented approach allows achieving better minimum distance and error correction capability while maintaining a structured and manageable encoding/decoding process.
Solution Approach 2:
The patent introduces asymmetric transformation matrices (different matrices for even and odd layers) and asymmetric freezing patterns (different freezing rules for different layers and positions). This asymmetry breaks the symmetry of classical polar codes, enabling improved minimum distance and error correction performance.
2Reliability
If more iterations are performed in decoding, then the error correction capability improves, but the decoding complexity increases
Solution Approach 1:
The encoding process performs preliminary actions by carefully designing the multi-layer transformation and freezing patterns to maximize minimum distance. This preliminary structuring enables the decoder to achieve good error correction with fewer iterations, reducing decoding complexity while maintaining reliability.
Solution Approach 2:
The patent changes key parameters of the code structure including the transformation matrices, freezing patterns, and layer configurations. These parameter changes are optimized to achieve better error correction capability with reduced decoding iterations, balancing reliability and complexity.
3Reliability
If dynamic freezing is implemented, then the code performance improves, but the encoding complexity increases
Solution Approach 1:
The patent implements dynamic freezing where the freezing pattern varies across different layers and positions rather than being static. This dynamic approach allows optimizing code performance by adapting which positions are frozen at each layer, while the systematic structure keeps encoding complexity manageable.
Solution Approach 2:
Different layers and positions have different freezing characteristics - some positions are frozen in certain layers but not in others. This local differentiation of freezing quality optimizes the overall code performance by tailoring the freezing pattern to the specific properties of each layer and position.
Data Source
AI summary
The disclosure relates to noiseless coding and, in particular, to the use of twisted polar code in data encoding and decoding. The disclosure increases the speed of encoding and/or decoding through the reduction in the number of iterations to be performed. The object is attained in method for encoding data, comprising the steps of: pre-coding, by a pre-coding module, data presented in the form of k-dimensional binary vector x, the pre-coding consists in computing u(0)=xW, where W is a matrix of dimension κ×2m, and m is a code parameter; performing, by the pre-coding module, m-layer twisted polarization transformation of vector u(0), wherein i-th transformation layer consists in partitioning vector u(i−1) into 2m−1 subvectors of length 2, multiplying the subvectors by matrix(1011),merging the resulting subvectors into one vector of dimension 2m.