Polar Code Construction With Prime-Dimension Kernels for Wireless BLER
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Solution Overview
Problem
Polar codes, despite their potential for reaching channel capacity, face challenges in practical implementation due to high encoding complexity and the need for long code lengths, which is impractical for wireless communications, and existing decoding methods like SC and SCL have limitations in error correction performance compared to LDPC and Turbo codes.
Innovation Solution
The use of polar encoding matrices GY and GZ of prime number dimension to encode input bits, producing a codeword that is transmitted, and employing a method involving these matrices to encode and decode polar codes efficiently, including the application of Successive Cancellation List (SCL) decoding with CRC bits for improved error correction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If polar codes are used to reach channel capacity, then error correction performance is improved, but encoding complexity increases
Solution Approach 1:
The patent segments the encoding process into two distinct stages: first applying a polar encoding matrix GY of prime number dimension Y to input bits to produce intermediate output bits, then applying a second polar encoding matrix GZ of prime number dimension Z to the output bits to produce the final codeword. This segmentation allows the system to achieve high error correction performance through multi-stage processing while managing encoding complexity by breaking down the overall transformation into smaller, more manageable matrix operations with prime dimensions that can be efficiently implemented.
2Reliability
If long code lengths are used to reach channel capacity, then error correction performance is improved, but implementation becomes impractical for wireless communications
Solution Approach 1:
The patent changes the dimensional parameters of the polar encoding matrices from conventional powers of 2 to prime numbers Y and Z. This parameter change allows the system to achieve effective code lengths suitable for wireless communications (avoiding excessively long codes) while maintaining strong error correction performance. The prime number dimensions provide a balance between code strength and implementation practicality, enabling efficient encoding and decoding operations at moderate code lengths.
3Productivity
If conventional SC or SCL decoding is used, then decoding efficiency is maintained, but error correction performance is limited compared to LDPC and Turbo codes
Solution Approach 1:
The patent employs a composite decoding approach that combines Successive Cancellation List (SCL) decoding with Cyclic Redundancy Check (CRC) verification. This composite method integrates the efficiency of SCL decoding with the error detection capability of CRC, achieving error correction performance comparable to LDPC and Turbo codes while maintaining decoding efficiency. The multi-stage polar encoding with prime dimensions works synergistically with this composite decoding strategy to overcome the limitations of conventional single-stage polar codes.
Data Source
AI summary
Input bits are encoded into codewords that include coded bits. Encoding involves applying a first set of polar encoding matrices GY of prime number dimension Y to the input bits to produce output bits, and applying a second set of polar encoding matrices GZ of prime number dimension Z to the output bits to produce the codeword. One or both of GX and GY could be non-2-by-2. Such kernel design and other aspects of code construction, including reliabilities and selection of sub-channels for code construction, non-CRC-aided error correction, and code shortening and puncturing, are discussed in further detail herein.