Polar Code Constraint Matrices for Lower-Complexity Decoding
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Solution Overview
Problem
The performance of polar subcodes in communication systems is unsatisfactory, particularly in the low SNR region, and they require complex specifications that are difficult to implement efficiently, especially for processors in communication systems.
Innovation Solution
The introduction of a processor-based encoder and decoder using a (n, k, d) parent polar code with helper codes, where the constraint matrix V is defined as (V0V100V2E), allowing for more freezing constraints and reducing decoding iterations and complexity, and a method for generating a compact specification of polar codes by determining frozen sets and their differences for a binary erasure channel.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If polar subcodes are used to improve minimum distance and decoding performance, then error correction capability is improved, but decoding complexity increases significantly
Solution Approach 1:
The constraint matrix V is segmented into multiple blocks (V0, V1, V2, E) where each block serves a specific function. This segmentation allows the decoder to process different parts of the code separately, reducing overall decoding complexity while maintaining the error correction capabilities provided by the polar subcode structure.
Solution Approach 2:
The patent employs dynamic frozen symbols that can be adjusted based on channel conditions and decoding progress. This dynamic adaptation allows the system to optimize between performance and complexity by selectively applying constraints during decoding, rather than using a fixed complex structure in all cases.
2Reliability
If more freezing constraints are applied to improve performance in low SNR region, then near-ML decoding performance is achieved, but number of iterations increases
Solution Approach 1:
The constraint matrix V is designed in advance with pre-calculated frozen symbol positions and constraint structures. This preliminary configuration allows the decoder to immediately apply optimized constraints without iterative search, achieving near-ML performance with fewer iterations by having the optimal freezing pattern prepared beforehand.
3Device complexity
If compact specification method is used to simplify code definition, then storage requirements are reduced, but code construction accuracy may be compromised
Solution Approach 1:
The patent uses a compact specification that captures the essential structure of the constraint matrix V through a simplified representation (block structure with parameters). This compact form acts as a template that can be efficiently stored and then expanded into the full code structure during implementation, maintaining accuracy while reducing storage requirements.
Data Source
AI summary
The disclosure relates to devices and methods implementing polar codes. For instance, the disclosure relates to an an encoder for encoding data, wherein the encoder comprises a processor configured to encode the data using a (n, k, d) parent polar code C into codewords c0n-1=u0n-1A subject to the constraints u0n-1VT=0, wherein u0n-1 denotes the data, whereinA=(1011)⊗m,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 the parent polar code the constraint matrix V1 of a first helper code C1 and the constraint matrix V2 of a second helper code C2.