Polar Subcode Encoder Without Polar Domination Constraint
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Solution Overview
Problem
Existing systematic polar subcode encoders face limitations due to the requirement of the polar domination property, which is difficult to satisfy, especially for polar subcodes where dynamic frozen indexes dominate information indexes, limiting their efficiency and applicability.
Innovation Solution
The proposed solution involves an efficient systematic encoder for polar subcodes that splits the input vector into six sections and applies specific formulas to each section, allowing for encoding without the need for the polar domination property, and optionally uses balance bits to enforce additional constraints, reducing complexity and increasing applicability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing systematic polar subcode encoders are used, then encoding can be performed, but the polar domination property requirement limits applicability and increases complexity
Solution Approach 1:
The input vector is divided into six distinct sections (first through sixth information vectors) based on different index sets. Each section is processed independently using specific formulas, allowing the encoder to handle cases where the polar domination property does not hold while maintaining systematic encoding capabilities.
Solution Approach 2:
Different encoding formulas are applied to different sections of the input vector based on their specific characteristics. The first and fourth sections use one formula, while the second, third, fifth, and sixth sections use another formula, optimizing the encoding process for each local region's requirements.
2Adaptability or versatility
If polar domination property is enforced, then systematic encoding is possible, but it restricts the types of polar subcodes that can be encoded
Solution Approach 1:
By segmenting the input vector into six sections and applying different formulas to each, the encoder can accommodate polar subcodes with dynamic frozen indexes that dominate information indexes, expanding the range of encodable codes without sacrificing systematic encoding properties.
Solution Approach 2:
The encoding approach changes based on the section being processed, using different mathematical formulas for different portions of the input vector. This parameter-based differentiation allows the encoder to handle various polar subcode configurations flexibly.
Data Source
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AI summary
Systems, devices, and methods for encoding information bits for storage, including obtaining an information vector comprising a plurality of information bits, a static frozen vector comprising a plurality of static frozen bits, and a constraints vector which indicates at least one constraint; partitioning the information vector into a first information vector and a second information vector; partitioning the static frozen vector into a first static frozen vector and a second static frozen vector; determining an input vector by applying a plurality of matrix operations to the first information vector, the second information vector, the first static frozen vector, the second static frozen vector, and the constraints vector; computing an output codeword of a polar subcode based on the input vector; and transmitting the output codeword to the storage device.