Asymmetric Polar Coding for Variable-Length Noisy Channels
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Traditional polar codes are limited by their fixed codeword length, which restricts their flexibility and efficiency in error correction, particularly in wireless communications, as they can only exist in lengths that are powers of 2, making them inadequate for practical applications requiring variable codeword lengths.
Innovation Solution
The implementation of asymmetric polar codes, which allow for the construction of polarizing linear block codes of any arbitrary length by connecting constituent polar codes of unequal lengths, enabling flexible codeword lengths and improved decoding performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional polar codes are used with fixed codeword lengths that are powers of 2, then the encoding and decoding structure is simple and regular, but the flexibility and adaptability to practical applications requiring variable codeword lengths is poor
Solution Approach 1:
The asymmetric polar code is segmented into two constituent polar codes of different lengths (N1 and N2). The input bit sequence is divided into two parts, each encoded by a separate constituent polar code, and then combined through additional polarizing stages. This segmentation allows the system to achieve variable codeword lengths while maintaining the structured approach of traditional polar codes.
Solution Approach 2:
The invention introduces asymmetry by using two constituent polar codes with unequal lengths (N1 ≠ N2) instead of the traditional symmetric structure where both constituents have equal lengths. This asymmetric structure enables flexible codeword length adjustment while preserving the polarization property and decoding efficiency through modified successive cancellation algorithms.
2Adaptability or versatility
If conventional solutions for variable codeword length are implemented, then flexibility is improved, but performance and complexity of decoding, encoding, or code design deteriorate
Solution Approach 1:
The system dynamically adjusts the lengths of the two constituent polar codes (N1 and N2) based on the desired total codeword length. The additional polarizing stages are adaptively configured to combine the constituents appropriately. This dynamic structure maintains optimal bit-error correction performance for each variable length configuration while preserving the polarization property that ensures reliable decoding.
3Adaptability or versatility
If asymmetric polar codes with arbitrary lengths are constructed by connecting constituent polar codes of unequal length, then codeword length flexibility is improved, but encoding and decoding complexity increases
Solution Approach 1:
The asymmetric polar code structure embeds two constituent polar codes of different lengths within a unified framework. The smaller constituent code is nested within the overall structure, and both are combined through additional polarizing stages that follow the same mathematical patterns as traditional polar codes. This nesting approach allows arbitrary length support while reusing existing polar code encoding and decoding algorithms with minimal modifications.
Data Source
AI summary
Systems and methods of communicating using asymmetric polar codes are provided which overcome the codeword length constraints of systems and methods of communicating that use traditional polar codes. Used herein, asymmetric polar codes refers to a polarizing linear block code of any arbitrary length that is constructed by connecting together constituent polar codes of unequal length. Asymmetric polar codes may be known by other names. In comparison to conventional solutions for variable codeword length, asymmetric polar codes may provide more flexibility, improved performance, and/or reduced complexity of decoding, encoding, or code design. The system and method provide a flexible, universal, and well-defined coding scheme and to provide sound bit-error correction performance and low decoding latency (compared with current length-compatible methods which can be used with current hardware designs). For the most part, the provided embodiments can be implemented with nearly all available current encoding/decoding polar code techniques.