Polar Code Constraint Matrix Design for Low-Complexity Decoding
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Solution Overview
Problem
The performance of polar subcodes is unsatisfactory, particularly in the low SNR region, and they require complex specifications that are difficult to implement efficiently in communication systems, with existing methods being either impractical or producing suboptimal results.
Innovation Solution
The implementation of recursive polar subcodes with a constraint matrix defined as V = [V0 V1 V2 E], where V1 and V2 are helper code constraint matrices, and additional freezing constraints are introduced to reduce decoding iterations and complexity, along with a compact specification method using binary erasure channel approximations to minimize the number of frozen symbols.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If polar subcodes are used to improve error correction performance, then reliability is improved, but decoding complexity increases
Solution Approach 1:
The constraint matrix V is segmented into helper code constraint matrices V1 and V2, allowing the decoding process to be divided into manageable stages. This segmentation reduces the overall decoding complexity while maintaining the error correction performance benefits of polar subcodes.
Solution Approach 2:
Freezing constraints are introduced in advance to reduce the number of iterations required during decoding. By pre-determining which symbols should be frozen based on error probability analysis, the decoder avoids unnecessary iterations, thereby reducing complexity while improving reliability.
2Reliability
If block sequential decoding is used to achieve near-ML decoding in low SNR region, then reliability is improved, but the number of iterations increases
Solution Approach 1:
Freezing constraints are predetermined based on error probability analysis before decoding begins. This preliminary action reduces the search space for the decoder, enabling near-ML performance to be achieved with fewer iterations in low SNR regions.
Solution Approach 2:
The error probability parameters Pji are used to dynamically determine which symbols should be frozen. By changing the freezing constraints based on these parameters, the system adapts to low SNR conditions and reduces the number of iterations required for near-ML decoding.
3Reliability
If comprehensive code specification is stored to ensure accurate code implementation, then reliability is improved, but memory requirements increase
Solution Approach 1:
The essential components of the code specification are extracted and stored, while redundant information is eliminated. By storing only the constraint matrix V (constructed from helper codes V1 and V2) and freezing constraints, the system maintains accurate code implementation with reduced memory requirements.
Solution Approach 2:
The code specification is prepared in advance by constructing the constraint matrix V from helper codes and determining freezing constraints. This preliminary preparation allows the actual transmission to use a compact representation, reducing memory storage requirements while ensuring accurate code implementation.
4Manufacturing precision
If density evolution method is used to compute error probabilities accurately, then manufacturing precision is improved, but complexity increases
Solution Approach 1:
Instead of using the computationally expensive density evolution method, the patent employs simpler approximation methods to compute error probabilities. These lighter computational objects are used for the purpose of determining freezing constraints, achieving sufficient accuracy without the high complexity of density evolution.
Solution Approach 2:
The patent changes the computational approach from exact density evolution to approximation methods. By adjusting the precision parameter to be sufficient rather than exact, the system achieves acceptable manufacturing precision for error probability computation with significantly reduced complexity.
Data Source
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AI summary
The invention relates to devices and methods implementing generalized polar codes with improved Hamming distance. For instance, the invention relates to an encoder (110) for encoding a data vector z, wherein the encoder (100) comprises a processor (111) configured to encode data z into a codeword c such that c0 n-1 = u0 n-1 A subject to the constraints u0 n-1 V T = 0, so that c=z. W.A where W is a matrix such that W.VT=0, wherein Formula (I) wherein F⊗m denotes the m-times Kronecker product of the matrix F with itself and wherein the constraint matrix V comprises in addition to the constraint matrix V0 of a parent polar code the constraint matrix V1 of a first helper code and the constraint matrix V2 of a second helper code C2.